# Answer to Question #3036 in Quantum Mechanics for Radu-Emanuel Mihai

Question #3036

A quantum particle is moving in a harmonic oscillator potential v(x)=m*omega^(2)*x^(2)/2.

The eigenstates are denoted by |n> while the wave functions are Psi n (x) = <x|n>.

At t=0, the system in the state: |Psi(t=0)>=A*sum from n of (1/sqrt(2))^2 | n >

Find the constant A, obtain the expression for the wave function Psi(x,t) = <x | Psi(t)> at a latter time, calculate the probability density |Psi(x,t)|^2 and the expectation value of the energy.

The eigenstates are denoted by |n> while the wave functions are Psi n (x) = <x|n>.

At t=0, the system in the state: |Psi(t=0)>=A*sum from n of (1/sqrt(2))^2 | n >

Find the constant A, obtain the expression for the wave function Psi(x,t) = <x | Psi(t)> at a latter time, calculate the probability density |Psi(x,t)|^2 and the expectation value of the energy.

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