A good example of time evolution of an operator is the position in x in 1-dimension. This simplified case allowsus to deal with the wave function as just a scalar so,< ¥\â\¥ >= ƒ ¥¹ â¥dxIn classical physics, we define momentum as pamdxdt--1 8²2m əx²Using the spatial representation in 1D, momentum is p = -2-ithe free particle Hamiltonian is, HCalculate the time derivative of and use the Schrodinger's Equation id/dt = Hy for a free particle toderive the quantum momentum as follow,=< p >d<â>dtmvx = m.

The expectation value of x can be written as: where is the complex conjugate of .In classical…

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