Question

Find ⟨p⟩ for the given wave function:

a) ⟨p⟩= 3ℏ/2a
b) ⟨p⟩= √3ℏ/a
c) ⟨p⟩= √3ℏ/2a
d) ⟨p⟩= 2ℏ/a

Answer 1

The expectation value of momentum is ⟨p⟩ = √3ħ/2a.

Step-by-step explanation:

A wave function (Ψ) is a mathematical function that relates the location of an electron at a given point in space (identified by x, y, and z coordinates) to the amplitude of its wave, which corresponds to its energy. Thus each wave function is associated with a particular energy E.where p is the momentum in one dimension, which can be any value from −∞ to +∞, and t is time. Analogous to the position case, the inner product of two wave functions Φ1(p, t) and Φ2(p, t) can be defined as: forms what is called the momentum basis.The expectation value of momentum, represented as ⟨p⟩, is given by the formula ⟨p⟩ = √3ħ/2a. This corresponds to option c) ⟨p⟩ = √3ħ/2a.