Unitarity And Tome Evolution Flashcards
1
Q
T-dependent wave function in Hilbert space
A
2
Q
Time dependent Schrödinger equation in Hilbert space
A
3
Q
Define exponential of operator
A
4
Q
Evolution operator
A
5
Q
Evolution by time t_1 followed by time t_2
A
6
Q
Adjoint of Evolutionary operator
A
7
Q
Standard solution to Schrödinger equation in Hilbert space
A
8
Q
A
9
Q
A
10
Q
A
11
Q
A
12
Q
Show unitarity of evolution operator
A
Important point is
e0 = 1
13
Q
Given 2 states |Ψ> and |Φ> € H
A
14
Q
Unitary time evolution preserves
A
Inner product
15
Q
Given H^^ and some initial state |Ψ(0)> how to find state |Ψ(t)> at some t€R
A
IMPORTANT ALGORITHM
-find eigenvalues E_n and orthonormal basis of eigenstates of H^^
- find expression for initial state in given basis
-act with evolutionary operator
