QUANTUM MECHANICS II
The Schrodinger wave equation 
General form
Normalization & Probability
Properties of valid wave functions
Boundary conditions
Time-Independent Schrödinger Wave
Equation
Stationary State
Comparison of Classical and Quantum
Mechanics
Newton’s second law can be derived from the Schrödinger
wave equation, so the latter is the more fundamental.
Classical mechanics only appears to be more precise because
it deals with macroscopic phenomena.
Newton’s second law (𝐹 ⃗ = 𝑑𝑝⃗/𝑑𝑡) and Schrödinger’s wave
equation are both differential equations.
Expectation Values
The expectation value is the expected result of the average of
many measurements of a given quantity.The expectation value
of x is denoted by <x>
Continuous Expectation Values
Momentum Operator
Position and Energy Operators
Infinite Square-Well Potential
Quantization
Quantized Energy
Finite Square-Well Potential
Penetration Depth
Three-Dimensional Infinite-Potential Well
Schrödinger wave equation
Degeneracy
A quantum state is degenerate when there is more than one wave
function for a given energy
Degeneracy results from particular properties of the potential energy
function that describes the system
A perturbation of the potential
energy can remove the degeneracy.
Simple Harmonic Oscillator
Parabolic Potential Well
Analysis of the Parabolic Potential Well
Barriers and Tunneling
Reflection and Transmission
The potentials and the Schrödinger wave equation for the three regions
The corresponding solutions are
Probability of Reflection and Transmission
Tunneling