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(2) Consider a particle moving in a harmonic oscillator potential along the x axis. The normalized energy eigenstates of the oscillator are denoted by $\Psi_n(x)$ where n is a non-negative integer. (a) At time t=0 particle is prepared in the state $\Phi(x) = A(\Psi_0(x) + (1+i)\Psi_1(x))$. Determine the value of A if the state is normalized. (b) What is the wave function at time t>0? (c) What is the expectation value of the position operator at time t? (d) Assume that the particle carries an electric charge Q and a uniform electric field E is applied to the system in addition to the harmonic potential. Find the new energy eigenvalues. Express the new eigenfunctions in terms of the functions $\Psi_n(x)$.

          (2) Consider a particle moving in a harmonic oscillator potential along the x axis. The normalized energy eigenstates of the oscillator are denoted by $\Psi_n(x)$ where n is a non-negative integer.
(a) At time t=0 particle is prepared in the state $\Phi(x) = A(\Psi_0(x) + (1+i)\Psi_1(x))$. Determine the value of A if the state is normalized.
(b) What is the wave function at time t>0?
(c) What is the expectation value of the position operator at time t?
(d) Assume that the particle carries an electric charge Q and a uniform electric field E is applied to the system in addition to the harmonic potential. Find the new energy eigenvalues. Express the new eigenfunctions in terms of the functions $\Psi_n(x)$.

(2) Consider a particle moving in a harmonic oscillator potential along the x axis. The normalized energy eigenstates of the oscillator are denoted by (x) where n is a non-negative integer.
(a) At time t=0 particle is prepared in the state Φ(x) = A(Ψ0(x) + (1+i)Ψ1(x)). Determine the value of A if the state is normalized.
(b) What is the wave function at time t>0?
(c) What is the expectation value of the position operator at time t?
(d) Assume that the particle carries an electric charge Q and a uniform electric field E is applied to the system in addition to the harmonic potential. Find the new energy eigenvalues. Express the new eigenfunctions in terms of the functions (x).

Added by Breanna H.

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