- #1
Sparky_
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Hello,I have been going through Griffiths’ Intro To Quantum Mechanics in an attempt to self-teach myself some quantum mechanics.
I am currently in section 3.4 (Generalized Statistical Interpretation)
I am seeing a “step” occur more than once. When I first came across it, while I didn’t understand “why”, I ignored it and moved on. I am now seeing it again. The deal is an inner product with a “prime variable” and a “non-primed” variable.
I believe it was first introduced in example 3.2 (second edition) page 103 where the eigenfunctions and eigenvalues of the momentum operator are calculated.
This is where the Dirac Delta Function first shows up.
Inner product of < fp’ | fp > = Dirac Delta
Within this example, I just went with it, not fully understanding why the need for p’
Now in section 3.4 pgs 106-109 Griffiths (and some others I found googling) just take it as an obvious step to have a prime variable and non-primed variable within the inner product
Page 107 – inner product of psi (wave function) with itself = 1
< psi | psi > =1
Next step show the linear combination formula with the index variable n. The left side of the inner product now has n’ and right side has n. (Equation 3.48)
Down a couple of lines, the expectation of Q: inner product of psi and Qpsi – again a n’ and n show up. (Equation 3.50)Bottom line, as you can see, I do not understand what’s going on and why it should be obvious to the reader to have a 2nd variable n’ or p’ ….Help?
Thanks
Sparky_
I am currently in section 3.4 (Generalized Statistical Interpretation)
I am seeing a “step” occur more than once. When I first came across it, while I didn’t understand “why”, I ignored it and moved on. I am now seeing it again. The deal is an inner product with a “prime variable” and a “non-primed” variable.
I believe it was first introduced in example 3.2 (second edition) page 103 where the eigenfunctions and eigenvalues of the momentum operator are calculated.
This is where the Dirac Delta Function first shows up.
Inner product of < fp’ | fp > = Dirac Delta
Within this example, I just went with it, not fully understanding why the need for p’
Now in section 3.4 pgs 106-109 Griffiths (and some others I found googling) just take it as an obvious step to have a prime variable and non-primed variable within the inner product
Page 107 – inner product of psi (wave function) with itself = 1
< psi | psi > =1
Next step show the linear combination formula with the index variable n. The left side of the inner product now has n’ and right side has n. (Equation 3.48)
Down a couple of lines, the expectation of Q: inner product of psi and Qpsi – again a n’ and n show up. (Equation 3.50)Bottom line, as you can see, I do not understand what’s going on and why it should be obvious to the reader to have a 2nd variable n’ or p’ ….Help?
Thanks
Sparky_