- #1
ambroochi
- 1
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The ground state wave-function of a 1-D harmonic oscillator is
$$
\psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}).
$$
a) find Average potential energy ?
$$
\overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2}
$$
b) find Average kinetic energy ?
$$
\overline{T} = \frac {\overline{p^2}}{2\mu}
$$
c) find momentum probability function ?
solving for a i got the answer as
$$
V=\frac{1}{4}\hbar\omega
$$
how do i find the momentum here ?
$$
\psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}).
$$
a) find Average potential energy ?
$$
\overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2}
$$
b) find Average kinetic energy ?
$$
\overline{T} = \frac {\overline{p^2}}{2\mu}
$$
c) find momentum probability function ?
solving for a i got the answer as
$$
V=\frac{1}{4}\hbar\omega
$$
how do i find the momentum here ?
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