Question

A harmonic oscillator with mass m and force constant k is in an excited state that has quantum number n.

1)

Let pmax=mvmaxx, where vmax is the maximum speed calculated in the Newtonian analysis of the oscillator. Derive an expression for pmax in terms of n, ℏ, k, and m.

Express your answer in terms of the variables n, k, m, and the constant ℏ

2)

Derive an expression for the classical amplitude A in terms of n, ℏ, k, and m.

Express your answer in terms of the variables n, k, m, and the constant ℏ.

3)

If Δx=A/√2 and Δpx=pmax/√2, what is the uncertainty product ΔxΔpx?

Express your answer in terms of the variable n and the constant ℏ.

Answer 1