One dimension in position representation:
(1)
In three dimensions In position representation, we define it by using the gradient, and so we see that
(2)
Video 1.
Position and Momentum from Wavefunctions by Faculty of Khan (2018)
Source. Proves in detail why the momentum operator is . The starting point is determining the time derivative of the expectation value of the position operator.

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  1. Position and momentum space
  2. Uncertainty principle
  3. Schrödinger equation
  4. Non-relativistic quantum mechanics
  5. Quantum mechanics
  6. Particle physics
  7. Physics
  8. Natural science
  9. Science
  10. Home

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