- #1
Geezer
- 293
- 0
Okay, I *know* that E and x are supposed to commute, but I'm stuck on one tiny portion when I work through this commutator...
So, here's my work. Feel free to point out my error(s):
[tex][E,x]\Psi=(i\hbar\frac{\partial}{\partial t}x-xi\hbar\frac{\partial}{\partial t})\Psi[/tex]
...which becomes...
[tex][E,x]\Psi=(i\hbar\frac{\partial x}{\partial t}\Psi+i\hbar x\frac{\partial\Psi}{\partial t}-i\hbar x\frac{\partial\Psi}{\partial t})[/tex]
So, here's my question: must [tex]\frac{\partial x}{\partial t}\Psi[/tex]
necessarily equal zero? Clearly it should if the commutator is going to be equal to zero...
Also, I recognize that something like dx/dt in quantum is fairly meaningless, but dx/dt is a lot lot <p>/m, which isn't meaningless in quantum...
Feel free to set me straight...
So, here's my work. Feel free to point out my error(s):
[tex][E,x]\Psi=(i\hbar\frac{\partial}{\partial t}x-xi\hbar\frac{\partial}{\partial t})\Psi[/tex]
...which becomes...
[tex][E,x]\Psi=(i\hbar\frac{\partial x}{\partial t}\Psi+i\hbar x\frac{\partial\Psi}{\partial t}-i\hbar x\frac{\partial\Psi}{\partial t})[/tex]
So, here's my question: must [tex]\frac{\partial x}{\partial t}\Psi[/tex]
necessarily equal zero? Clearly it should if the commutator is going to be equal to zero...
Also, I recognize that something like dx/dt in quantum is fairly meaningless, but dx/dt is a lot lot <p>/m, which isn't meaningless in quantum...
Feel free to set me straight...