- #1
Nafreyu
- 4
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Hi, I'm totally lost here...Quantum physics seems to be just incomprehensible to me! Hope someone can help me out! That would be great!
(a) A spin system with 2 possible states, described by
(E1 0)=H
(0 E2)
with eigenstates [tex]\vec{\varphi}[/tex]1 = [tex]\left\langle[/tex]1[tex]\right,0\rangle[/tex] and [tex]\vec{\varphi}[/tex]2 =[tex]\left\langle[/tex]0[tex]\right,1\rangle[/tex] and Eigenvalues E1 and E2. Verify this. How do these eigenstates evolve in time?
(b) consider the state [tex]\vec{\psi}[/tex] = a1 [tex]\vec{\varphi}[/tex]1 + a2 [tex]\vec{\varphi}[/tex]2 with real coefficients a1, a2 and total probability equal to unity. How does the state [tex]\vec{\psi}[/tex] evolve in time?
I only know that [tex]\vec{\psi}[/tex] must solve the Schroedinger equation to show the time dependence of a1 and a2 and a12 + a22 must be equal to 1. Other than that I'm really totally lost! This is one of 4 tasks I need to finish to pass this course, I can do the other 3, but this one I just don't get. So please help! I would be very grateful...
Homework Statement
(a) A spin system with 2 possible states, described by
(E1 0)=H
(0 E2)
with eigenstates [tex]\vec{\varphi}[/tex]1 = [tex]\left\langle[/tex]1[tex]\right,0\rangle[/tex] and [tex]\vec{\varphi}[/tex]2 =[tex]\left\langle[/tex]0[tex]\right,1\rangle[/tex] and Eigenvalues E1 and E2. Verify this. How do these eigenstates evolve in time?
(b) consider the state [tex]\vec{\psi}[/tex] = a1 [tex]\vec{\varphi}[/tex]1 + a2 [tex]\vec{\varphi}[/tex]2 with real coefficients a1, a2 and total probability equal to unity. How does the state [tex]\vec{\psi}[/tex] evolve in time?
The Attempt at a Solution
I only know that [tex]\vec{\psi}[/tex] must solve the Schroedinger equation to show the time dependence of a1 and a2 and a12 + a22 must be equal to 1. Other than that I'm really totally lost! This is one of 4 tasks I need to finish to pass this course, I can do the other 3, but this one I just don't get. So please help! I would be very grateful...