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PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (2²), (p²), and the product (a)(p*).

PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (2²), (p²), and the product (a)(p*).

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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 \(\sqrt{\langle x^2 \rangle \langle p^2 \rangle}\).
Transcribed Image Text:**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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Solution:

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

Advanced Physics homework question answer, step 1, image 1

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

Advanced Physics homework question answer, step 1, image 2

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