The half harmonic oscillator's ground state wave function

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SUMMARY

The ground state wave function for the half harmonic oscillator is defined as x * exp(-x^2/2). This function is valid exclusively for positive x values. The discussion highlights the importance of checking the parity of wave functions, noting that some functions exhibit even parity, others odd parity, and some none at all. In asymmetric potential wells, stationary state wave functions do not necessarily possess symmetry about the origin or any specific point.

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Apashanka
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For the half harmonic oscillator the ground state wave function is of the form x*exp(-x^2/2)
But sir how to check it's parity and with respect to with point
As this function is valid for positive x only
Thank you
 
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Some functions have even parity, some have odd parity and some have none. Which do you think this is?
 
In an asymmetric potential well, the stationary state wavefunctions don't need to have a symmetry about the origin or any other point.
 

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