1 00:00:00,060 --> 00:00:02,280 so when people first showed that matter 2 00:00:02,280 --> 00:00:04,620 particles like electrons can have 3 00:00:04,620 --> 00:00:06,839 wavelengths and when dubrow's showed 4 00:00:06,839 --> 00:00:09,210 that the wavelength is Planck's constant 5 00:00:09,210 --> 00:00:11,820 over the momentum people were like cool 6 00:00:11,820 --> 00:00:14,309 it's pretty sweet but you know someone 7 00:00:14,309 --> 00:00:15,389 was like wait a minute 8 00:00:15,389 --> 00:00:18,210 if this particle has wave-like 9 00:00:18,210 --> 00:00:21,300 properties and it has a wavelength what 10 00:00:21,300 --> 00:00:24,510 exactly is waving what is this wave 11 00:00:24,510 --> 00:00:26,760 we're even talking about conceptually 12 00:00:26,760 --> 00:00:29,130 it's a little strange I mean a water 13 00:00:29,130 --> 00:00:31,500 wave we know what that is it's a bunch 14 00:00:31,500 --> 00:00:33,899 of water that's oscillating up and down 15 00:00:33,899 --> 00:00:36,510 a wave on a string we know what that is 16 00:00:36,510 --> 00:00:38,790 the string itself is moving up and down 17 00:00:38,790 --> 00:00:41,100 and it extends through space but it's 18 00:00:41,100 --> 00:00:43,559 hard to imagine how is this electron 19 00:00:43,559 --> 00:00:46,530 having a wavelength and what is the 20 00:00:46,530 --> 00:00:49,140 actual wave itself so physicists were 21 00:00:49,140 --> 00:00:51,120 grappling with this issue trying to 22 00:00:51,120 --> 00:00:53,730 conceptually understand how to describe 23 00:00:53,730 --> 00:00:56,399 the wave of the electron they wanted to 24 00:00:56,399 --> 00:00:58,739 do two things they wanted a mathematical 25 00:00:58,739 --> 00:01:00,840 description for the shape of that wave 26 00:01:00,840 --> 00:01:03,180 and that's called the wave function so 27 00:01:03,180 --> 00:01:04,949 this wave function gives you a 28 00:01:04,949 --> 00:01:07,200 mathematical description for what the 29 00:01:07,200 --> 00:01:08,869 shape of the wave is so different 30 00:01:08,869 --> 00:01:11,010 electron systems are going to have 31 00:01:11,010 --> 00:01:13,290 different wave functions and this is 32 00:01:13,290 --> 00:01:16,350 this is psy it's the symbol for the wave 33 00:01:16,350 --> 00:01:19,740 function so this is psy the size symbol 34 00:01:19,740 --> 00:01:22,590 it's a function of X so at different 35 00:01:22,590 --> 00:01:25,170 points in X it may have a large value 36 00:01:25,170 --> 00:01:27,780 and may have a small value this function 37 00:01:27,780 --> 00:01:29,729 would give you the mathematical shape of 38 00:01:29,729 --> 00:01:31,439 this wave so I was one of the things 39 00:01:31,439 --> 00:01:33,090 they were trying to determine but they 40 00:01:33,090 --> 00:01:35,220 also wanted to interpret it like what is 41 00:01:35,220 --> 00:01:37,740 this wave function even mean so we've 42 00:01:37,740 --> 00:01:40,079 got two problems we want a mathematical 43 00:01:40,079 --> 00:01:41,909 description of the wave and we want to 44 00:01:41,909 --> 00:01:43,890 interpret what is this wave even mean 45 00:01:43,890 --> 00:01:46,619 now the person that gave us the 46 00:01:46,619 --> 00:01:49,140 mathematical description of this wave 47 00:01:49,140 --> 00:01:52,170 function was Irwin Schrodinger so 48 00:01:52,170 --> 00:01:54,590 Schrodinger is this guy right here 49 00:01:54,590 --> 00:01:56,189 Schrodinger's right here 50 00:01:56,189 --> 00:01:58,439 he wrote down Schrodinger's equation and 51 00:01:58,439 --> 00:01:58,950 his 52 00:01:58,950 --> 00:02:01,469 aim now is basically synonymous with 53 00:02:01,469 --> 00:02:03,240 quantum mechanics because this is 54 00:02:03,240 --> 00:02:05,430 arguably the most important equation in 55 00:02:05,430 --> 00:02:07,500 all of quantum mechanics there's a bunch 56 00:02:07,500 --> 00:02:09,389 of partial derivatives in here and 57 00:02:09,389 --> 00:02:11,849 Planck's constants but the important 58 00:02:11,849 --> 00:02:13,890 thing is that it's got the wave function 59 00:02:13,890 --> 00:02:15,780 in here now if you've never seen partial 60 00:02:15,780 --> 00:02:17,880 derivatives or calculus it's okay all 61 00:02:17,880 --> 00:02:19,860 you need to know for our purposes today 62 00:02:19,860 --> 00:02:22,739 in this video is that this equation is a 63 00:02:22,739 --> 00:02:25,769 way to crank out the mathematical wave 64 00:02:25,769 --> 00:02:28,230 function what is this function that 65 00:02:28,230 --> 00:02:30,660 gives us the shape of the wave as a 66 00:02:30,660 --> 00:02:32,370 function of X and you can imagine 67 00:02:32,370 --> 00:02:34,980 plotting this on some graph so once you 68 00:02:34,980 --> 00:02:37,530 solve for this sigh as a function of X 69 00:02:37,530 --> 00:02:39,810 you could plot what this looks like 70 00:02:39,810 --> 00:02:41,730 maybe it looks something like this and 71 00:02:41,730 --> 00:02:43,739 who knows it could do all kinds of stuff 72 00:02:43,739 --> 00:02:45,180 maybe it looks like that but 73 00:02:45,180 --> 00:02:47,160 Schrodinger's equation is the way you 74 00:02:47,160 --> 00:02:49,410 can get this wave function so 75 00:02:49,410 --> 00:02:51,420 Schrodinger gave us a way to get the 76 00:02:51,420 --> 00:02:53,430 mathematical wave function but we also 77 00:02:53,430 --> 00:02:55,530 wanted to interpret it what does this 78 00:02:55,530 --> 00:02:57,440 even mean to say that this wave function 79 00:02:57,440 --> 00:03:00,180 represents the electrons is still 80 00:03:00,180 --> 00:03:02,010 strange what does that mean 81 00:03:02,010 --> 00:03:03,780 Schrodinger tried to interpret it this 82 00:03:03,780 --> 00:03:05,850 way he said okay maybe maybe this 83 00:03:05,850 --> 00:03:08,639 electron really is like smudged out in 84 00:03:08,639 --> 00:03:11,310 space and it's charge is kind of 85 00:03:11,310 --> 00:03:13,489 distributed in different places 86 00:03:13,489 --> 00:03:16,590 Schrodinger wanted to interpret this 87 00:03:16,590 --> 00:03:20,370 wave function as charge density and I 88 00:03:20,370 --> 00:03:21,870 mean it's kind of a reasonable thing to 89 00:03:21,870 --> 00:03:22,350 do 90 00:03:22,350 --> 00:03:24,090 the way you get a water wave is by 91 00:03:24,090 --> 00:03:26,639 having water spread out through space so 92 00:03:26,639 --> 00:03:28,709 maybe the way you get an electron wave 93 00:03:28,709 --> 00:03:31,109 is to have the charge of the electron 94 00:03:31,109 --> 00:03:33,540 spread out through space but this 95 00:03:33,540 --> 00:03:35,579 description didn't work so well which is 96 00:03:35,579 --> 00:03:38,010 kind of strange Schrodinger invented 97 00:03:38,010 --> 00:03:39,720 this equation he came up with this 98 00:03:39,720 --> 00:03:41,819 equation but he couldn't even interpret 99 00:03:41,819 --> 00:03:44,430 what he was describing correctly it took 100 00:03:44,430 --> 00:03:46,260 someone else it took a guy named Max 101 00:03:46,260 --> 00:03:49,079 Born to give us the interpretation we go 102 00:03:49,079 --> 00:03:52,019 with now for this wave function Max Born 103 00:03:52,019 --> 00:03:54,000 said nah don't interpret it as the 104 00:03:54,000 --> 00:03:55,980 charge density what you should do is 105 00:03:55,980 --> 00:03:58,590 interpret this sy is giving you a way to 106 00:03:58,590 --> 00:04:00,870 get the probability of finding the 107 00:04:00,870 --> 00:04:03,780 electron at a given point in space so 108 00:04:03,780 --> 00:04:06,150 Max Born said this if you find your sigh 109 00:04:06,150 --> 00:04:07,560 like he said go ahead and use 110 00:04:07,560 --> 00:04:09,480 Schrodinger's equation use it 111 00:04:09,480 --> 00:04:11,780 get the sigh once you have 112 00:04:11,780 --> 00:04:14,720 what you do is you square this function 113 00:04:14,720 --> 00:04:16,970 so take the absolute value square it and 114 00:04:16,970 --> 00:04:18,440 what that's going to give you is the 115 00:04:18,440 --> 00:04:22,040 probability of finding the electron at a 116 00:04:22,040 --> 00:04:24,290 given point now technically it's the 117 00:04:24,290 --> 00:04:27,140 probability density but for our purposes 118 00:04:27,140 --> 00:04:28,760 you can pretty much just think about 119 00:04:28,760 --> 00:04:30,980 this as the probability of finding the 120 00:04:30,980 --> 00:04:33,170 electron at a given point so if this was 121 00:04:33,170 --> 00:04:35,030 our wave function in other words Max 122 00:04:35,030 --> 00:04:37,010 Born would tell us that points where 123 00:04:37,010 --> 00:04:39,020 it's zero these points right here where 124 00:04:39,020 --> 00:04:41,480 the value is zero there is a zero 125 00:04:41,480 --> 00:04:43,460 percent chance you're going to find the 126 00:04:43,460 --> 00:04:45,290 electron there points where there's a 127 00:04:45,290 --> 00:04:49,070 large value of sy be it positive or 128 00:04:49,070 --> 00:04:51,260 negative there's going to be a large 129 00:04:51,260 --> 00:04:53,600 probability of finding the electron at 130 00:04:53,600 --> 00:04:56,150 that point and we could say the odds of 131 00:04:56,150 --> 00:04:57,650 finding the electron at a given point 132 00:04:57,650 --> 00:04:59,930 here are going to be largest for this 133 00:04:59,930 --> 00:05:02,360 value of x right here because that's the 134 00:05:02,360 --> 00:05:04,640 point for which the wave function has 135 00:05:04,640 --> 00:05:07,730 the greatest magnitude but you won't 136 00:05:07,730 --> 00:05:10,220 necessarily find the electron there if 137 00:05:10,220 --> 00:05:12,800 you repeat this experiment over and over 138 00:05:12,800 --> 00:05:16,010 you may find the electron here once you 139 00:05:16,010 --> 00:05:17,720 may find it over here you may find it 140 00:05:17,720 --> 00:05:19,970 there next time you have to keep taking 141 00:05:19,970 --> 00:05:21,410 measurements and if you keep taking 142 00:05:21,410 --> 00:05:22,520 measurements you'll get this 143 00:05:22,520 --> 00:05:23,870 distribution where you find a lot of 144 00:05:23,870 --> 00:05:27,110 them here a lot of them there a lot of 145 00:05:27,110 --> 00:05:28,820 them here and a lot of them here always 146 00:05:28,820 --> 00:05:30,290 where there's these peaks you get more 147 00:05:30,290 --> 00:05:32,419 of them then you would have at other 148 00:05:32,419 --> 00:05:34,760 points where the values were smaller you 149 00:05:34,760 --> 00:05:36,530 build up a distribution that's 150 00:05:36,530 --> 00:05:39,050 represented by this wave function so the 151 00:05:39,050 --> 00:05:40,790 wave function does not tell you where 152 00:05:40,790 --> 00:05:42,650 the electron is going to be it just 153 00:05:42,650 --> 00:05:44,600 gives you the probability and 154 00:05:44,600 --> 00:05:47,000 technically the square of it gives you 155 00:05:47,000 --> 00:05:48,350 the probability of finding the electron 156 00:05:48,350 --> 00:05:50,360 somewhere so even it points down here 157 00:05:50,360 --> 00:05:52,220 with the wave function has a negative 158 00:05:52,220 --> 00:05:53,990 value I mean you can't have a negative 159 00:05:53,990 --> 00:05:57,050 probability you square that value that 160 00:05:57,050 --> 00:05:59,210 gives you the probability of finding the 161 00:05:59,210 --> 00:06:01,010 electron in that region so in other 162 00:06:01,010 --> 00:06:02,780 words let's get rid of all this let's 163 00:06:02,780 --> 00:06:06,200 say we sold some Schrodinger equation or 164 00:06:06,200 --> 00:06:08,240 we were just handed a wave function and 165 00:06:08,240 --> 00:06:09,590 we were told it looks like this and 166 00:06:09,590 --> 00:06:11,390 we're asked where are you most likely to 167 00:06:11,390 --> 00:06:13,729 find the electron well the value of the 168 00:06:13,729 --> 00:06:15,919 wave function is greatest at this point 169 00:06:15,919 --> 00:06:18,020 here so you'd be most likely to find the 170 00:06:18,020 --> 00:06:20,270 electron in this region right here you'd 171 00:06:20,270 --> 00:06:22,430 have no shot of finding it right there 172 00:06:22,430 --> 00:06:23,930 you'd have pretty good odds of finding 173 00:06:23,930 --> 00:06:25,340 it right here or 174 00:06:25,340 --> 00:06:27,110 here but you'd have the greatest chance 175 00:06:27,110 --> 00:06:29,180 of finding it in this region right here 176 00:06:29,180 --> 00:06:31,070 so you have to repeat this measurement 177 00:06:31,070 --> 00:06:33,650 many times in quantum mechanics one 178 00:06:33,650 --> 00:06:35,600 measurement doesn't verify that you've 179 00:06:35,600 --> 00:06:37,430 got the right wave function because if I 180 00:06:37,430 --> 00:06:39,169 do one experiment and measure one 181 00:06:39,169 --> 00:06:41,210 electron Boop I might find the electron 182 00:06:41,210 --> 00:06:42,410 right there that doesn't really tell me 183 00:06:42,410 --> 00:06:44,630 anything I have to repeat this over and 184 00:06:44,630 --> 00:06:47,330 over to make sure the relative frequency 185 00:06:47,330 --> 00:06:49,940 of where I'm finding electrons matches 186 00:06:49,940 --> 00:06:52,280 the wave function I'm using to model 187 00:06:52,280 --> 00:06:54,500 that electron system so that's what the 188 00:06:54,500 --> 00:06:56,479 wave function is that's what it can do 189 00:06:56,479 --> 00:06:59,000 for you although if I were you I'd still 190 00:06:59,000 --> 00:07:00,800 be unsatisfied I'd be like wait a minute 191 00:07:00,800 --> 00:07:03,290 okay that's fine and good wave function 192 00:07:03,290 --> 00:07:05,660 can give us the probability or the 193 00:07:05,660 --> 00:07:07,550 probability density of finding the 194 00:07:07,550 --> 00:07:09,229 electron in a given region but we 195 00:07:09,229 --> 00:07:11,150 haven't answered the question what is 196 00:07:11,150 --> 00:07:14,600 waving here and what exactly is this 197 00:07:14,600 --> 00:07:16,729 wave function is this a physical object 198 00:07:16,729 --> 00:07:19,389 sort of like a water wave or even an 199 00:07:19,389 --> 00:07:21,500 electromagnetic wave or is this just 200 00:07:21,500 --> 00:07:23,840 some mathematical trickery that we're 201 00:07:23,840 --> 00:07:25,600 using that has no physical 202 00:07:25,600 --> 00:07:28,100 interpretation other than giving us 203 00:07:28,100 --> 00:07:30,860 information about where the electron is 204 00:07:30,860 --> 00:07:32,900 going to be and I've got good news and 205 00:07:32,900 --> 00:07:33,830 bad news 206 00:07:33,830 --> 00:07:36,800 the bad news is that people still don't 207 00:07:36,800 --> 00:07:39,289 agree on how to interpret this wave 208 00:07:39,289 --> 00:07:41,660 function yes they know that the square 209 00:07:41,660 --> 00:07:43,220 of it gives you the probability of 210 00:07:43,220 --> 00:07:45,380 finding the electron in some region but 211 00:07:45,380 --> 00:07:47,270 people differ on how they're supposed to 212 00:07:47,270 --> 00:07:49,370 interpret it past that point for 213 00:07:49,370 --> 00:07:52,160 instance is this wave function the wave 214 00:07:52,160 --> 00:07:54,800 function of a single electron or is this 215 00:07:54,800 --> 00:07:57,020 wave function really the wave function 216 00:07:57,020 --> 00:08:00,700 of a system an ensemble of electrons all 217 00:08:00,700 --> 00:08:02,780 similarly prepared that you're going to 218 00:08:02,780 --> 00:08:05,000 do the experiment on in other words does 219 00:08:05,000 --> 00:08:07,010 it describe one electron or only 220 00:08:07,010 --> 00:08:09,710 described a system of electrons does it 221 00:08:09,710 --> 00:08:11,630 not describe the electron at all but 222 00:08:11,630 --> 00:08:14,210 only our measurement of the electron and 223 00:08:14,210 --> 00:08:16,610 what happens to this wave function when 224 00:08:16,610 --> 00:08:18,710 you actually measure the electron when 225 00:08:18,710 --> 00:08:20,210 you measure the electron you find it 226 00:08:20,210 --> 00:08:22,340 somewhere and at that moment there's no 227 00:08:22,340 --> 00:08:24,530 chance of finding it over here at all so 228 00:08:24,530 --> 00:08:26,690 does the act of measuring the electron 229 00:08:26,690 --> 00:08:29,599 cause some catastrophic collapse in this 230 00:08:29,599 --> 00:08:31,910 wave function that's not described by 231 00:08:31,910 --> 00:08:34,010 Schrodinger's equation these and many 232 00:08:34,010 --> 00:08:36,500 more questions are still debated and not 233 00:08:36,500 --> 00:08:37,820 completely understood 234 00:08:37,820 --> 00:08:38,690 that's the bad 235 00:08:38,690 --> 00:08:40,909 News the good news is that we don't 236 00:08:40,909 --> 00:08:43,190 really need to understand that to make 237 00:08:43,190 --> 00:08:46,160 progress everyone knows how to use the 238 00:08:46,160 --> 00:08:48,350 wave function to get the probabilities 239 00:08:48,350 --> 00:08:50,089 of measurements you can have your 240 00:08:50,089 --> 00:08:52,220 favorite interpretation but luckily 241 00:08:52,220 --> 00:08:54,290 pretty much regardless of how you 242 00:08:54,290 --> 00:08:56,660 interpret this wave function as long as 243 00:08:56,660 --> 00:08:58,189 you're using it correctly to get the 244 00:08:58,189 --> 00:09:00,170 probabilities of measurements you can 245 00:09:00,170 --> 00:09:02,389 continue making progress testing 246 00:09:02,389 --> 00:09:04,850 different models and correlating data to 247 00:09:04,850 --> 00:09:06,410 the measurements that people make in the 248 00:09:06,410 --> 00:09:07,870 lab now I'm not saying that 249 00:09:07,870 --> 00:09:09,980 interpretations of this wave function 250 00:09:09,980 --> 00:09:12,199 are not important people have tried 251 00:09:12,199 --> 00:09:14,360 cracking this nut for over a hundred 252 00:09:14,360 --> 00:09:16,910 years and it's resisted maybe that's 253 00:09:16,910 --> 00:09:19,100 because it's a waste of time or maybe 254 00:09:19,100 --> 00:09:20,990 it's because the difficulty of figuring 255 00:09:20,990 --> 00:09:23,329 this out is so great that whoever does 256 00:09:23,329 --> 00:09:25,189 it will go down in history as one of the 257 00:09:25,189 --> 00:09:27,560 great physicists of all time it's hard 258 00:09:27,560 --> 00:09:29,839 to tell right now but what's undebatable 259 00:09:29,839 --> 00:09:31,550 is that for about a hundred years now 260 00:09:31,550 --> 00:09:34,370 we've been able to make progress with 261 00:09:34,370 --> 00:09:36,439 quantum mechanics even though we differ 262 00:09:36,439 --> 00:09:39,110 on how exactly to interpret what this 263 00:09:39,110 --> 00:09:41,449 wavefunction really represents so 264 00:09:41,449 --> 00:09:43,310 recapping the wavefunction gives you the 265 00:09:43,310 --> 00:09:45,410 probability of finding a particle in 266 00:09:45,410 --> 00:09:48,380 that region of space specifically the 267 00:09:48,380 --> 00:09:50,480 square of the wave function gives you 268 00:09:50,480 --> 00:09:53,389 the probability density of finding a 269 00:09:53,389 --> 00:09:55,610 particle at that point in space this 270 00:09:55,610 --> 00:09:57,829 almost everyone has agreed upon whether 271 00:09:57,829 --> 00:09:59,540 the wave function has deeper 272 00:09:59,540 --> 00:10:00,410 implications 273 00:10:00,410 --> 00:10:03,170 besides this people differ but that 274 00:10:03,170 --> 00:10:04,970 hasn't yet stopped us from applying 275 00:10:04,970 --> 00:10:07,339 quantum mechanics correctly in a variety 276 00:10:07,339 --> 00:00:00,000 of different scenarios