4 Ladder operators Flashcards
(8 cards)
1
Q
What are the units for the position for the ladder operators?
A
(ℏ/mω)1/2
2
Q
What are the units for the momentum for the ladder operators?
A
(ℏmω)1/2
3
Q
What is the Hamlitonian for the ladder operators?
A
H = 1/2 (P2 + X2)
Where P and X are the momentum and position operators
4
Q
What are the ladder operators?
A
R+ = P + iX
R- = P - iX
Where P and X are the momentum and position operators
5
Q
How do the ladder operators define th3 hamiltonian?
A
H = 1/2 (R+R- + 1) = 1/2 (R-R+ - 1)
6
Q
What are the commutations of the
ladder and Hamiltonian operators?
A
[R+,H] = -R+
[R-,H] = +R-
7
Q
What do the ladder operators do?
A
Move up and down on the ladder of states
8
Q
What are the energy levels for the ladder operators?
A
En = n + 1/2
