PhysLean Documentation

PhysLean.QuantumMechanics.OneDimension.Operators.Momentum

Momentum operator #

In this module we define:

We show that plane waves are generalized eigenvectors of the momentum operator.

The momentum operator on functions ℝ → ℂ #

The momentum operator is defined as the map from ℝ → ℂ to ℝ → ℂ taking ψ to - i ℏ ψ'.

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    The momentum operator on Schwartz maps #

    The parity operator on the Schwartz maps is defined as the linear map from 𝓢(ℝ, ℂ) to itself, such that ψ is taken to fun x => - I ℏ * ψ' x.

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      Generalized eigenvectors of the momentum operator #

      The momentum operator is self adjoint #