Recent content by Gary Roach

Homework Statement Problem 2.21 from Introduction to Electrodynamics, David J. Griffiths, Third Edition. Find the potential inside and outside a uniformly charged solid sphere who's radius is R and whose total charge is q. Use infinity as your reference point. Homework Equations...

Thank you Vela. I had fogotten that. That makes sense. It's too bad that Griffiths didn't point this out. Generally the text is great, especially for self study but he sloughs thing sometimes.

Yes at x=a, x=0 Also not sure where this should go. It is a clarification of the textbook not a homework problem. At least this was my reasoning. I've been wrong before. Gary

Homework Statement In David Griffiths Introduction to Quantum Mechanics (2nd ed.), page 32 he normalizes a time independent wave function to get the coefficient A. He dropped the sine part of the integration with no explanation. What is the justification. Homework Equations The time...

Thanks diazona Just what I needed. It's nice to know that I'm not just dense. Gary R

Homework Statement The concept of a scalar potential is reasonably straight forward. It is the energy needed to move to a point from some arbitrary reference point, the reference point being the origin for most mechanical problems and infinity for most electromagnetic problems.And of course...

Finallly. The normalization of the eigenvectors of \Lambda fixed the problem. U^\dagger*U now = I, U^\dagger*\Lambda * U = diagonal with eigenvalues in the diagonal. The same with \Omega. Question: Does this work only because the two matrices share a common eigenvector? Gary R. and thank...

I think I need to back up on this problem. Per Shankar: If \Lambda is a Hermitian matrix, there exists a unitary matrix U (built out of the eigenvectors of \Lambda such that U^\dagger \Lambda U is diagonalized. So let's use Lambda from above since it is Hermitian. And we have the...

I'm still thinking about your replies (reading like crazy). I haven't disappeared. My Linear Algebra seems to be a bit rusty. I really appreciate the help. Gary R.

Homework Statement From Principles of Quantum Mechanics, 2nd edition by R Shankar, problem 1.8.10: By considering the commutator, show that the following Hermitian matrices may be simultaneously diagonalized. Find the eigenvectors common to both and verify that under a unitary transformation...

I rechecked the text. The actual statement is "up to a scale". I goofed in the second message. Sorry Gary R.

This is from the proof of theorem 13 page 44 of Principles of Quantum Mechanics- 2nd edition by R Shanker. The up to scale is a direct quote. Thanks all for the help. Gary R.

I guess I wasn't specific enough in my question. Sorry. The definition I would like is as the phrase applies to the following statement: ie \Lambda|\omega_i> is an eigenvector of \Omega with eigenvalue \omega_i . Since the vector is unique \underline{up\ to\ a\ scale}...

Homework Statement What is the meaning of the phrase "up to a scale" as applied to eigenvectors in quantum mechanics. Homework Equations None The Attempt at a Solution N/A did an extensive search of the web and my texts. No joy.

Oops. There seems to be a hole here in my knowledge. Oh well, back to the books. Thanks for the prompt reply. Gary R.