1. Lecture 2: A physical interpretation of QM Part I: Meaning of the wave function; the Born rule

2. Schrödinger equation
The Nobel Prize in Physics 1933 was awarded jointly to Erwin Schrödinger and Paul Adrien Maurice Dirac "for the discovery of new productive forms of atomic theory."

3. Born interpretation
The Nobel Prize in Physics 1954 was divided equally between
Max Born "for his fundamental research in quantum mechanics,
especially for his statistical interpretation of the wavefunction"

4. So, what is the wave-function?
It may be a wrong question to ask, as the wave-function is a mathematical construct
(one among several others) that allows us to calculate what we are interested in
(observables, i.e., something we can actually measure).
Find the wave-function
which satisfies a closed
Eq and determines X
Quantum observable,
X, at t=0
Know:
X, at a later time t=T
Want to know:
No closed
equation for X…
We certainly have seen such auxiliary concepts elsewhere in physics. For example:
Neither scalar nor vector potential is directly observable, which does not surprise
us, neither should we be surprised by the wave-function…

5. Lecture 2: A physical interpretation of QM Part II: Operators

6. Appearance of operators in Schrödinger’s “derivation”
Experimental fact: quantum electrons
may exhibit wave-like properties
Assume that they may be described
by a plane-wave function:
We have to reconcile it with
Hence the free Schrodinger equation
Generalize it to
with
We can write it as
if we identify,

7. Expectation values

8. A physical interpretation of quantum theory Part III: Time-independent Schrödinger Eq. Eigenvalue problems

9. Getting rid of the time derivative, when it’s not needed

10. A simple (mathematical) example of an eigenvalue problem

11. Operators, eigenvalues, and eigenvectors in QM: summary

12. Lecture 2: A physical interpretation of QM Part IV: Superposition principle; Dirac notations; representations

13. Superposition principle in quantum mechanics

14. Simple reminder from linear algebrax’ y’ x y

15. How to choose a basis/representation