QUANTUM MECHANICS II

The Schrodinger wave equation schro schroo

General form gebnral

Normalization & Probability norma

Properties of valid wave functions

Boundary conditions boundary cond

Time-Independent Schrödinger Wave
Equation ttt

Stationary State tvt

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> za

Continuous Expectation Values zx

Momentum Operator cvb

Position and Energy Operators bnv

Infinite Square-Well Potential nm

Quantization mmm

Quantized Energy bn nhy

Finite Square-Well Potential bhyt

bnh

Penetration Depth a

Three-Dimensional Infinite-Potential Well

Schrödinger wave equation b

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 c

Parabolic Potential Well aa aaa

Analysis of the Parabolic Potential Well bb ccc

Barriers and Tunneling zxv

Reflection and Transmission

The potentials and the Schrödinger wave equation for the three regions v

The corresponding solutions are tae

Probability of Reflection and Transmission asas

Tunneling rm f