The half harmonic oscillator's ground state wave function

[Apashanka]

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

 

[kuruman]

Some functions have even parity, some have odd parity and some have none. Which do you think this is?

 

[hilbert2]

In an asymmetric potential well, the stationary state wavefunctions don't need to have a symmetry about the origin or any other point.