1. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Oct 29, 2012
Karine Chesnel

2. Homework this week: HW #16 Friday Nov 4 Pb 4.1, 4.2, 4.3, 4.5 Phys 451
Announcements
Homework this week:
HW #16 Friday Nov 4
Pb 4.1, 4.2, 4.3, 4.5

3. Phys 451
Schrödinger equation
in 3 dimensions x y z

4. Which one of the following quantities
Phys 451
Quiz 18
Which one of the following quantities
is not correct? A. B. C. D. E.
Pb 4.1

5. Phys 451
Position- momentum
in 3 dimensions
Pb 4.1

6. Phys 451
Schrödinger equation
in 3 dimensions
now
Laplacian

7. Schrödinger equation in 3 dimensions Phys 451 General solution
Each stationary
state verifies

8. Spherical coordinates
Phys 451
Spherical coordinates z
radius
polar angle
azimuthal angle r y x
Laplacian

9. Schrödinger equation in spherical coordinates
Phys 451
Schrödinger equation in
spherical coordinates x y z r
Separation of variables

10. Schrödinger equation in spherical coordinates
Phys 451
Schrödinger equation in
spherical coordinates x y z r
The radial equation
The angular equation

11. The angular equation Phys 451 y z r Further separation of variables: x
Azimuthal equation:
m integer
q equation:

12. The angular equation Phys 451 y x z r Physical condition l,m integers
Solution:
Legendre function
Legendre polynomial
Physical condition
l,m integers

13. The angular equation Phys 451 y z r x Legendre function Solution:
are polynoms in cosq
(multiplied by sinq if m is odd)

14. Spherical harmonics l m Phys 451 y z r x Normalization
Azimuthal quantum number
Magnetic quantum number l m x
Normalization
Simulation: