 #1
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Hello!
I am studying the Sakurai book on Quantum mechanics and I am doing a problem. I have the solutions to the problems to help me understand the material better but I do not understand this solution.
SEE "Sakurai Problem 1" in attachments
K is the propagator in wave mechanics.
2. Solution
SEE "Sakurai Problem 1" in attachments
There are a few parts of this solution that I do not understand.
1.) In the first part it states that "The probability is.."
[tex]P(Ea')=exp(βEa')/Z[/tex]
Probability of what? It doesn't actually tell me what the "Partition function" is or means. Isn't the propagator an operator? I thought in order to have a probability you need to have a state in mind.
2.) I also do not understand why the ground state energy is equal to that summation "U=...." in the next line.
3.) I do not understand the first change of variables in the differential, da' = L/2π dk
If anyone could help me understand this, it would be much appreciated! :D
I am studying the Sakurai book on Quantum mechanics and I am doing a problem. I have the solutions to the problems to help me understand the material better but I do not understand this solution.
Homework Statement
SEE "Sakurai Problem 1" in attachments
K is the propagator in wave mechanics.
2. Solution
SEE "Sakurai Problem 1" in attachments
There are a few parts of this solution that I do not understand.
1.) In the first part it states that "The probability is.."
[tex]P(Ea')=exp(βEa')/Z[/tex]
Probability of what? It doesn't actually tell me what the "Partition function" is or means. Isn't the propagator an operator? I thought in order to have a probability you need to have a state in mind.
2.) I also do not understand why the ground state energy is equal to that summation "U=...." in the next line.
3.) I do not understand the first change of variables in the differential, da' = L/2π dk
If anyone could help me understand this, it would be much appreciated! :D
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