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## Main Question or Discussion Point

if we have two non-interacting particles of mass M in a one-dimensional harmonic oscillator potential of frequency ω, with the wavefunction defined as:

$$\Psi\left(x_1,x_2\right) = \psi_n\left(x_1\right) \psi_m\left(x_2\right)$$

where x_1 and x_2 are two particle co-ordinates. and ψ_n is the nth harmonic oscillator eigenfunction.

then:

a) will:

$$\psi_n(x_1)= (\frac{\frac{M*\omega}{\hbar}}{\pi})^{1/4}*H_n(x_1)*e^{-\frac{M*x_1^2*\omega}{2*h}}$$

or will it be in this format:

$$\frac{1}{\sqrt{2^n*n!}}*(\frac{m*\omega}{\pi*\hbar})^{1/4}*e^{-\frac{M*x_1^2*\omega}{2*\hbar}}*H_n(\sqrt{\frac{m*\omega}{\hbar}}*x)$$

b) What is <x_1-x_2>??

$$\Psi\left(x_1,x_2\right) = \psi_n\left(x_1\right) \psi_m\left(x_2\right)$$

where x_1 and x_2 are two particle co-ordinates. and ψ_n is the nth harmonic oscillator eigenfunction.

then:

a) will:

$$\psi_n(x_1)= (\frac{\frac{M*\omega}{\hbar}}{\pi})^{1/4}*H_n(x_1)*e^{-\frac{M*x_1^2*\omega}{2*h}}$$

or will it be in this format:

$$\frac{1}{\sqrt{2^n*n!}}*(\frac{m*\omega}{\pi*\hbar})^{1/4}*e^{-\frac{M*x_1^2*\omega}{2*\hbar}}*H_n(\sqrt{\frac{m*\omega}{\hbar}}*x)$$

b) What is <x_1-x_2>??

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