# Quantum Oscillator

## Homework Statement

Problem 8.
1. Express the distance $$x_c$$ as a function of the mass $$m$$ and the restoring
parameter $$c$$ used in Problem 7.

(Problem 7.
1. Calculate the energy of a particle subject to the potential $$V(x) = V_0 + cx^2/2$$ if the particle is in the third excited state.
2. Calculate the energy eigenvalues for a particle moving in the potential
$$V(x) = cx^2/2 + bx$$.)

Quantum Mechanic. Chapter 3. Daniel B. Res.

## Homework Equations

$$H=\frac{p^2}{2m}+\frac{m\omega ^2}{2}x^2$$

## The Attempt at a Solution

I cannot understand what is actually meant by this parameter $$x_c$$ and how to approach the problem.

vela
Staff Emeritus
Homework Helper
It might help if you provided the complete problem statement for problem 8. The reference to problem 7 just means c is a spring constant; it doesn't say anything about what xc is supposed to represent.

Problem 8.
1. Express the distance $$x_c$$ as a function of the mass $$m$$ and the restoring
parameter $$c$$ used in Problem 7.
2. If $$c$$ is multiplied by 9, what is the separation between consecutive eigenvalues?
3. Show that $$x_c$$ is the maximum displacement of a classical particle moving
in a harmonic oscillator potential with an energy of $$\hbar\omega/2$$.

vela
Staff Emeritus