- #1
Nemanja989
- 79
- 2
Hi :),
recently I was thinking whether every bound state is only real or imaginary, not mixture? Since all bound states have degeneracy of level one, if we suppose that [itex]ψ=ψ_{r}+iψ_{i}[/itex], then [itex]ψ_{r}[/itex] and [itex]ψ_{i}[/itex] must be linearly dependent as in opposite case there would be a bound state with degeneracy of level two.
Is this type reasoning good or not?
In every single example that I have seen or was doing numerically bound state wave function was always real.
Also, degeneracy level is derived through ordinary Schrodinger equation. What about non-linear Schrodinger equation? Does in this case every bound state correspond to only one wave function, or there is degeneracy of higher level?
Thanks in advance :)
recently I was thinking whether every bound state is only real or imaginary, not mixture? Since all bound states have degeneracy of level one, if we suppose that [itex]ψ=ψ_{r}+iψ_{i}[/itex], then [itex]ψ_{r}[/itex] and [itex]ψ_{i}[/itex] must be linearly dependent as in opposite case there would be a bound state with degeneracy of level two.
Is this type reasoning good or not?
In every single example that I have seen or was doing numerically bound state wave function was always real.
Also, degeneracy level is derived through ordinary Schrodinger equation. What about non-linear Schrodinger equation? Does in this case every bound state correspond to only one wave function, or there is degeneracy of higher level?
Thanks in advance :)