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Quantum Mechanics


  1. State Space - Provides basic definitions including bras, kets, scalar products, Hilbert space etc.
  2. Gaussian state - An example of expectations using a state which has a Gaussian probability distribution.
  3. Calculate <x2> - An example of calculating an expectation using a Gaussian distribution. 
  4. Calculate <p2>  Another example of calculating an expectation using a Gaussian distribution. 
  5. Postulates of Quantum Mechanics
  6. Tensor Product of Two States - The tensor product of two states is also a state.
  7. Harmonic Oscillator
  8. Harmonic Oscillator Eigenfunctions
  9. Conservation of Probability - The continuity equation is derived for the conservation of probability
  10. Expectation [TBD]
  11. N Operator - Describes the creation and annihilation operators.
  12. Probability - A discussion of the basics of probability as it applies to quantum theory.
  13. Step Potentials - Find the wave-function, transmission and reflection coefficients for a step potential
  14. Function of an Operator - Defines the meaning of function of operator.
  15. Time-Energy Uncertainty Relation - Describes the time evolution of energy expectation.