- #1
MaximumTaco
- 45
- 0
Defining the state [itex]| \alpha > [/itex] such that:
[tex]| \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C};[/tex]
Now, [itex]| \alpha >[/itex] is an eigenstate of the lowering operator [itex]\hat{a}[/itex], isn't it?
In other words, the statement that [itex] \hat{a} | \alpha >\ =\ \alpha | \alpha > [/itex] is true, right?
(for the eigenvalue [itex]\alpha[/itex]?)
Is that the correct use of the Dirac notation?
How might one go about proving the above?
[tex]| \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C};[/tex]
Now, [itex]| \alpha >[/itex] is an eigenstate of the lowering operator [itex]\hat{a}[/itex], isn't it?
In other words, the statement that [itex] \hat{a} | \alpha >\ =\ \alpha | \alpha > [/itex] is true, right?
(for the eigenvalue [itex]\alpha[/itex]?)
Is that the correct use of the Dirac notation?
How might one go about proving the above?
Last edited: