Canonical Systems Derivations
Canonical-system derivations are the workbench of wave mechanics. They show how boundary conditions, normalizability, coordinate choices, and symmetry turn the formal postulates into spectra and wavefunctions.
Foundations
Section titled “Foundations”- Coordinate Representation
- Hamiltonians in Coordinate Space
- Time-Independent Schrödinger Equation
- Probability Current
- Continuity Equation
- Boundary Conditions
One-Dimensional Systems
Section titled “One-Dimensional Systems”- Infinite Square Well
- Delta-Function Potential
- Finite Square Well
- Rectangular Barrier Tunneling
- Reflection and Transmission Coefficients
Free Motion and Oscillators
Section titled “Free Motion and Oscillators”- Momentum Eigenstates
- Free-Particle Propagator
- Gaussian Wave Packets
- Harmonic Oscillator: Ladder Operators
- Harmonic Oscillator: Differential Equation
- Hermite Functions
Three-Dimensional and Electromagnetic Systems
Section titled “Three-Dimensional and Electromagnetic Systems”- Angular and Radial Separation
- Density of States: First Encounter
- Radial Schrödinger Equation
- Hydrogen Atom
- Landau Levels
- Degeneracy of Landau Levels
References
Section titled “References”- D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
- R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
- L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed., Pergamon, 1977.