Quantum Mechanics SWBQs

• Helping Find the Equation of Motion for a Particle on a Ring

• What's the Energy of a Free Particle?

• What's the Hamiltonian of a Free Particle?

• Determining Radial Wave Functions

• Examining the Particle Confined to a Ring

• Operating on Spherical Harmonics

• Using Rydberg's Formula

• Drawing Bound States

• Showing Two Vectors are Eigenstates in a 2-Well System

• Naming Types of Periodic Systems

• Practice with an LCAO

• Single Simple Harmonic Oscillator

• Angular Momentum Review

• Completeness Relation for a Three-Level System

• Changing Basis with Completeness in Dirac Notation

• Computing Outer Products

• Properties of Outer Products

• Projection Operator in Dirac Notation

• Computing Inner Products

• Drawing the Probability Distribution of a Normalized Wave Function

• Drawing the Plot of a Normalized Wave Function

• Angular Momentum Review

• Interpret Delta Function Wave Function (a,b,c,d)

• Physically Interpreting the Plot of a Wave Function

• Basic Probability (Conceptual)

• Ket to Matrix (y/n)

• Ket to Matrix in New Basis

• Momentum Eigenvalue by Dimensions (a,b,c,d)

• Guessing Momentum as a Differential Operator (a,b,c,d)

• Expectation Value of Momentum with Wave Functions

• Expectation Value of Momentum with Wave Functions (a,b,c,d)

• Normalization from Probability Density Graph (y/n)

• Normalization from Wave Function Graph (y/n)

• Outer Products in Matrix Notation

• Outer Product Acting on a Wave Function

• Factoring Overall Phases

• SWBQ Sequence

• Interpreting Stern-Gerlach with Dirac Notation

• Interpreting Stern-Gerlach with Dirac Notation

• Converting a Simple Spin-1 Bra-ket Function into Matrix Notation

• Guessing the Form of Spin Along x in Terms of z

• Converting a Simple Spin-half Bra-ket State into its Matrix Representation in another Basis

• Calculating the $S^{2}$ Matrix

• Collapsing a Quantum State

• The $S_{z}$ Operator

• The Hamiltonian in V(x)

• Dimensions of the Wave Function

• Wave Function Manipulations

• Wave Functions and Probability Density Implications (a,b,c,d)

• The Hamiltonian in V(x)

• Understanding Eigenvalue Equations

• Expectation Values in the Wave Function Representation

• Wave Functions in an Infinite Potential Well

• Normalizing Wave Functions

• Orthogonality in the Wave Function Representation

• Recalling Schroedinger's Equation

• Calculating Expectation Values in Superposition States