- #1

iamalexalright

- 164

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## Homework Statement

Given an initial ave function [tex]\Psi(x)[/tex] at t=0, and a complete set of energy eigenfunctions [tex]\varphi_{n}(x)[/tex] with corresponding eigenenergies E_n for a particle, and no other information, in therms of the given find:

**a. Find the state of the particle at a later time**

Solution: [tex]\Psi(x,t) = T(t)*\varphi_{n}(x) = e^{-iE_{n}t/\hbar}\varphi_{n}(x)[/tex]

b. what is the probability that a measurement of energy will yield a particular value E_n?

[tex]<E> = \sum_{n}C_{n}P(C_n)[/tex]

Where P is the probability but I don't know where to go from here.

c. Find an expression for the average energy of the particle in terms of the enrgy eigenvalues:

[tex]<E>=1/n \sum_{i=1}^{n}E_{n}[/tex]

All seems right besides b? Any hints on b?

Solution: [tex]\Psi(x,t) = T(t)*\varphi_{n}(x) = e^{-iE_{n}t/\hbar}\varphi_{n}(x)[/tex]

b. what is the probability that a measurement of energy will yield a particular value E_n?

[tex]<E> = \sum_{n}C_{n}P(C_n)[/tex]

Where P is the probability but I don't know where to go from here.

c. Find an expression for the average energy of the particle in terms of the enrgy eigenvalues:

[tex]<E>=1/n \sum_{i=1}^{n}E_{n}[/tex]

All seems right besides b? Any hints on b?