Question

A particle of mass $m$ in the harmonic oscillator potential (Equation 2.44 starts out in the state $$\Psi(x, 0)=A(1-2 \sqrt{\frac{m \omega}{\hbar}} x)^{2} e^{-\frac{m \omega}{2 \hbar} x^{2}},$$ for some constant $A.$ (a) Determine $A$ and the coefficients $c_{n}$ in the expansion of this state in terms of the stationary states of the harmonic oscillator. (b) In a measurement of the particle's energy, what results could you get, and what are their probabilities? What is the expectation value of the energy? (c) At a later time $T$ the wave function is $$\Psi(x, T)=B(1+2 \sqrt{\frac{m \omega}{\hbar}} x)^{2} e^{-\frac{m \omega}{2 \hbar} x^{2}},$$ for some constant $B$. What is the smallest possible value of $T$ ?

          A particle of mass $m$ in the harmonic oscillator potential (Equation 2.44 starts out in the state $$\Psi(x, 0)=A(1-2 \sqrt{\frac{m \omega}{\hbar}} x)^{2} e^{-\frac{m \omega}{2 \hbar} x^{2}},$$ for some constant $A.$
(a) Determine $A$ and the coefficients $c_{n}$ in the expansion of this state in terms
of the stationary states of the harmonic oscillator.
(b) In a measurement of the particle's energy, what results could you get, and what are their probabilities? What is the expectation value of the energy?
(c) At a later time $T$ the wave function is $$\Psi(x, T)=B(1+2 \sqrt{\frac{m \omega}{\hbar}} x)^{2} e^{-\frac{m \omega}{2 \hbar} x^{2}},$$ for some constant $B$. What is the smallest possible value of $T$ ?

Added by Eva S.

Question

Please give Ace some feedback