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--- classes:2009:fall:phys4101.001:q_a_1111 [2009/11/10 20:14] – gebrehiwet
+++ classes:2009:fall:phys4101.001:q_a_1111 [2009/11/16 22:20] (current) – yk
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-===== Nov 11 (Wed)  =====
+===== Nov 11 (Wed) Radial Wave Function (finite well, hydrogen) =====
 **Return to Q&A main page: [[Q_A]]**\\
 **Q&A for the previous lecture: [[Q_A_1109]]**\\
@@ Line 20: / Line 20: @@
 Thanks!
+=== liux0756 11/11/2009 4:00pm ===
+Yes, simultaneous eigenstates are important. Generally speaking if two operators do not have simultaneous eigenstates, then they can't be measured at the same time. For example, x and p do not have simultaneous eigenstates, so we can't get the exact value of x and p at the same time: <math>\delta x \delta p \ge \hbar/2</math> But angular momentum <math>l^2</math> and <math>l_z</math> have common eigenstates and in those states both of them can have exact measurement.
+====Dagny====
+Basic question: How do we go (what's the process) from dxdydz to <math>r^2sin\theta</math><math>dr</math><math>d\theta</math><math>d\phi</math>
+===Blackbox 11/12/2009 12:15pm===
+The process is simple, dxdydz=dv for the cartesian coordinate system. In similar way, dv for the spherical coordinate system is <math>dr*rd\theta*rsin\theta d\phi</math>. It may be easily understood if you look at the sherical coordinate system plot from any EM refernece book.
+===Daniel Faraday 11/12 10:30pm===
+Wait a second: the sin term isn't squared in dV, is it? I thought dV was just
+<math>r^2sin\theta dr d\theta d\phi</math>  ??
+===Dagny===
+Correct!
+====Blackbox 11/12/2009 11:50am====
+I just forgot,, Could anyone tell me about the unit of <math> k=\frac{sqrt{2mE}}{\hbar} </math>? Thanks,
+===liux0756===
+The unit of k is [length]^-1. Because momentum <math>p=\hbar k</math>, angular momentum <math> L= n \hbar = momentum*length </math>, so k is [length]^-1.
+====Dagny====
+What is the very detailed process for the transformation of the gradient operator from cartesian to spherical coordinates? Just one operator term is fine, like del/delx. (Because I'm just interested in the process and also how we come about this process.) I've found a couple of website examples on how to do it, but nothing that provides a clear explanation.
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 **Q&A for the previous lecture: [[Q_A_1109]]**\\
 **Q&A for the next lecture: [[Q_A_1113]]**

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