- #1
physics2004
- 25
- 0
I've been trying to solve some questions using dirac notation, and most seem to be pretty straight forward (once you set everything up) but i always seem to get stuck when i try to find the matrix element and i can't seem to find the proper way to express the eigenstates given...
so for example we got some practice problems where we have to find the matrix element <a|U(t,tb)|b>. A and B are just position eigenstates and U(t,tb) is just the time evolution operator just:exp((-i*H/h)*(t-tb))
H = Hamiltonian
h = H bar (i.e 1.05e-34)
tb= intial time
t = final timeI get that the time operator just shifts the parameter t from tb to t, but all the other ones I've done i was given all the eigenstates. For example, griffiths 3.23 where you atleast have a orthonormal basis to start with and then you just need to find the eigenvalues and vectors. But for this question we are expected to find the matrix element given abstract position eigenstates? not quite sure how to get started. Maybe iam just struggling with dirac notation in general as i just learned it not to long ago, but iam not quite sure how to approach the question.
Thanks any help would be appreciated, also there's a similar question but its with the displacement operator but i figure if i can get this one i should be able to try the other one too.
so for example we got some practice problems where we have to find the matrix element <a|U(t,tb)|b>. A and B are just position eigenstates and U(t,tb) is just the time evolution operator just:exp((-i*H/h)*(t-tb))
H = Hamiltonian
h = H bar (i.e 1.05e-34)
tb= intial time
t = final timeI get that the time operator just shifts the parameter t from tb to t, but all the other ones I've done i was given all the eigenstates. For example, griffiths 3.23 where you atleast have a orthonormal basis to start with and then you just need to find the eigenvalues and vectors. But for this question we are expected to find the matrix element given abstract position eigenstates? not quite sure how to get started. Maybe iam just struggling with dirac notation in general as i just learned it not to long ago, but iam not quite sure how to approach the question.
Thanks any help would be appreciated, also there's a similar question but its with the displacement operator but i figure if i can get this one i should be able to try the other one too.