# Outline for 3 Midterm Exam A. Schrödinger Equation in 1D

```Outline for 3rd Midterm Exam
A. Schr&ouml;dinger Equation in 1D
1. Separation of variables
2. time-dependence: eiwt , separation constant E
3. time-independent equation: stationary states, quantization of energy
4. restrictions on wave function ψ; normalization
B. Infinite Square Well
1. harmonic solutions (sine/cosine)
2. boundary conditions lead to quantized energy
3. complete wave function Ψ(x,t)
C. Finite Square Well, Barriers, Harmonic Oscillators
1. Nonzero ψ in classically forbidden regions
2. Qualitative solutions
3. Transmission and Reflection coefficients
D. Expectation values and operators
E. Schr&ouml;dinger Equation in 3D
1. Separation of variables, multiple quantum numbers
2. infinite square well, quantized energy states
F. Hydrogen Atom
1. Separation of variables, quantum numbers (n, l, m), quantize E and L
2. properties of wave functions
3. energy level diagram (n and l)
G. Electron Spin
1. definition of spin and magnetic moment
2. Stern-Gerlach experiment
H. Spin-Orbit Coupling
1. vector picture of adding angular momenta, calculate j
2. spectroscopic notation for atoms: nLj
I. Electronic configurations
1. Pauli Exclusion Principle
2. Electron shells; filled shells and Noble gasses
3. Periodic Table
Equations to Learn. All equations in the Chapter Summary boxes; If other equations
are needed, I will give them to you.
1. Schr&ouml;dinger Equation
2. Uncertainty Principle
3. de Broglie relations
4. Normalization condition
Skills and Techniques. You should be able to:
1. Sketch wave functions for any one-dimensional potential
2. Discuss the interpretation of wave functions; compute expectation values
3. Sketch an energy-level diagram
4. Understand origin of quantization of angular momentum and energy
5. Understand levels and degeneracies in hydrogen atom, including spin
6. Know how to combine angular-momentum quantum numbers ```