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In the quantum harmonic oscillator problem, how would one go about calculating

$$\langle n|\frac{1}{X^2}|n\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only, where $X\propto a + a^{\dagger}$ is a linear combination of the raising and lowering operators?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.

In the quantum harmonic oscillator problem, how would one go about calculating

$$\left\langle n\left|\frac{1}{X^2}\right|n\right\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only, where $X\propto a + a^{\dagger}$ is a linear combination of the raising and lowering operators?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.

In the quantum harmonic oscillator problem, how would one go about calculating

$$\langle n|\frac{1}{X^2}|n\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only, where X is a linear combination of the raising and lowering operators?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.

In the quantum harmonic oscillator problem, how would one go about calculating

$$\langle n|\frac{1}{X^2}|n\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only, where $X\propto a + a^{\dagger}$ is a linear combination of the raising and lowering operators?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.

In the quantum harmonic oscillator problem, how would one go about calculating

$$\langle n|\frac{1}{X^2}|n\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.

In the quantum harmonic oscillator problem, how would one go about calculating

$$\langle n|\frac{1}{X^2}|n\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only, where X is a linear combination of the raising and lowering operators?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.