- #1
Safder Aree
- 42
- 1
Homework Statement
Does the n = 2 state of a quantum harmonic oscillator violate the Heisenberg Uncertainty Principle?
Homework Equations
$$\sigma_x\sigma_p = \frac{\hbar}{2}$$
The Attempt at a Solution
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I worked out the solution for the second state of the harmonic oscillator.
$$\frac{1}{\sqrt{2}}(\frac{mw}{\pi\hbar})^{1/4}(\frac{1}{\hbar})(e^{\frac{-mwx^2}{2\hbar}}(2mwx^2 - \hbar)$$
Should I be solving for standard deviation of position and momentum? Or is there another way to do this problem. I'm not sure what the next step is. Thank you for the guidance.