In the first lecture, we guessed in, in 
some sense the form of the Schrodinger 
equation relying on a few very basic, 
experimental facts, such as wave particle 
duality and the dispersion relation of a 
free electron. 
But we didn't talk too much about the 
meaning of the main object that appears 
in this equation the wavefunction, which 
was introduced in an ad hoc fashion. 
So today, I'm going to talk about the 
actual physical interpretation of quantum 
theory formulated this week. 
And we are also going to introduce the, a 
few very important standard notations and 
conventions that are going to be used 
throughout the course and also that are 
routinely used in the standard literature 
on the subject. 
So, here is the Schrodinger equation, 
once again we're going to see it very 
often in this course. 
And I'm also showing here the, a part of 
the first page of the original paper by 
Schrodinger, published in December of 
1926. 
And it's actually very interesting how 
Schrodinger came up with this work and 
this equation. 
So, apparently the story started back in 
1925 or so, when he was working under 
Debye, and Debye had just read a paper 
about de Broglie, where de Broglie was 
introducing his wave particle duality 
ideas. 
So, he got interested in these ideas and 
suggested Schrodinger to give a seminar 
on de Broglie's work. 
So apparently, Schrodinger actually 
dismissed this at first, saying that he 
didn't even want to think about such a 
silly theory. 
But he had to give in because well, Debye 
was effectively his supervisor. 
And so, he was looking into de Broglie's 
work, trying to present it in a more 
mathematically sophisticated form. 
And in doing so, he came up with the 
Schrodinger equation essentially, as we 
now know it. 
And which brought him the worldwide 
recognition and a Nobel Prize in Physics 
in 1933. 
So, another important thing that 
Schrodinger did was that he used his 
equation to solve a very important 
problem of the charged particle and the 
cool-down potential, which essentially 
describes a quantum hydrogen atom. 
And he found the energy level structure 
which is which was consistent with the 
with de Broglie's atom. 
And so, actually, Charles Clark is going 
to talk about the the solution later in 
this course but I'm just going to mention 
here that this was indeed very important 
and it was a clear smoking gun that 
Schrodinger was on the right track. 
But according to Debye at least quite 
interestingly that Schrodinger didn't 
really quite understand the true meaning 
of his own work. 
He actually dismissed about the 
importance of it at first. 
So, I don't know if it was just Debye 
being jealous or it, it was true. 
But certainly if you actually read the 
original paper by Schrodinger, you don't 
see too much insight into the true 
physical interpretation of his own 
equation. 
And the correct interpretation of 
Schrodinger's equation was developed very 
shortly after Schrodinger's work by Max 
Born. 
perhaps, actually, I should say and note 
the correct interpretation but the 
commonly accepted interpretation because 
scientists actually have been arguing 
about the interpretation up to these 
days. 
And some are still not convinced that the 
Born interpretation and the Born, Born 
rule that I'm going to present is the 
only a correct view of Quantum Physics. 
But certainly, this Born rule is the 
cornerstone of a, a standard quantum 
theory, and it is indeed consistent with 
all experimental data as we know it at 
this stage. 
Now before formulating this rule I would 
like to make a few general comments about 
Quantum Physics and make, make them in 
contrast to classical Physics. 
So, in classical Physics, if we have a 
classical system, let's say, this is a 
closed classical system with some closed 
classical particles moving around. 
And if we know everything about the 
system, let's say,we know all the 
coordinates of all the particles of a 
certain moment of time, and all the 
velocities at a certain moment of time. 
Then classical theory predicts with 
absolute certainty, every, the result of 
any conceivable experiment that is going 
to happen in the future, which is 
determined by, let's say trajectories of 
particles at any subsequent moment of 
time. 
And these deter, determine all possible 
outcomes of all possible experiments. 
Now, this is the classical system. 
So, the truth about the quantum system, 
so if you look at the, the actual 
association with quantum systems, so if 
you have a quantum system like that, say, 
with some wavefunction of psi. 
So, even if we know everything possible 
about this quantum system, that is, if we 
know psi, and if we know all the forces, 
everything about this system, we still 
cannot possibly predict with certainty, 
the outcomes of well-posed experiments. 
Let's say, if we have some detectors 
here, and they measure well, let's say 
detect electrons or some other particles. 
So, even if we know everything about the 
quantum electrons, we still cannot 
predict for sure which detector is 
going to pick up electrons at certain 
moment of time. 
And so, this uncertainty and is intrinsic 
to Quantum Physics and there is no way 
around it. 
And so, Born, Born realized it and he 
also found a way to quantify his 
uncertainty using the wavefunction. 
And here's what we know now is the Born 
rule, is written here, so basically he 
proposed, and afterwards it was 
confirmed. 
again, by comparing with experimental 
data, that the absolute value of the 
wavefunction, as related as certain 
position in space, and a certain moment 
of time gives a probability density of 
finding a quantum particle described by 
this wavefunction in this this position 
and at this moment of time t. 
Well, the probability itself is going to 
of psi, the absolute value of psi squared 
times the volume the elementary volume in 
the vicinity of a certain point. 
This work of Max Born turned out to be 
extremely influential and groundbreaking 
and he eventually received a Nobel Prize 
for these ideas in part in 1954. 
As a matter of fact, he should have 
received this award much earlier. 
He was nominated by Albert Einstein 
actually back in the 30s. 
but he didn't get it due to some 
political reasons. 
In but in any case, this probabilistic 
interpretation was and actually remains 
very remarkable feature of Quantum 
Physics, which is also a source of 
confusion often times. 
And I'm actually supposed to tell you, 
now about this probabilistic property 
being a mystery of Quantum Physics and 
something which we will never be able to 
understand. 
But I would actually argue otherwise that 
there is, in fact, nothing mysterious 
about it. 
If, by mysterious, we mean something that 
is not consistent with our everyday 
intuition, everyday experience, so 
actually uncertainty is a part of our 
everyday life whether we are dealing with 
a sporting event or any other event in 
our life, we can predict with certainty 
if we know everything how it's going to 
turn out. 
And so I don't see a reason to demand 
from size deterministic answers. 
And nature just doesn't work in this way, 
and so we should just accept this fact 
and get used to it.