Answered: PROBLEM 2 Calculate the probability… | bartleby

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**Problem 2**

Calculate the probability distribution of momenta \( p \) for a 1D oscillator in the ground state (\( n = 0 \)). Calculate the mean square dispersions \(\langle x^2 \rangle\), \(\langle p^2 \rangle\), and the product \(\sqrt{\langle x^2 \rangle \langle p^2 \rangle}\).

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The ground state is n =0. The position and momentum operator in terms of raising and lowering operator is given as

The raising and lowering operators acts on n-state is given as

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