- #1
cooev769
- 114
- 0
I know about symmetry and antisymmetry and so on, but a thought that I had never considered just hit me. If we had two fermions in the triplet symmetric spin state and hence therefore an antisymmetric spatial state, for example a harmonic oscillator in the first excited state must be one in state n and one in k:
psi = 1/(sqr root 2)( n1k2 - n2k1 )
But this wavefunction is clearly different from
psi = 1/(sqr root 2)( n2k1 - n1k2 )
Clearly it is just the exchange operator applied to the wave function, i can see that the expectation values will always be the same, so can you just choose how you order these and in which order they go?
psi = 1/(sqr root 2)( n1k2 - n2k1 )
But this wavefunction is clearly different from
psi = 1/(sqr root 2)( n2k1 - n1k2 )
Clearly it is just the exchange operator applied to the wave function, i can see that the expectation values will always be the same, so can you just choose how you order these and in which order they go?