Timeline for Why do $H$ and $L^2$ commute in spherically symmetric potential?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2015 at 12:43 | vote | accept | a00 | ||
| Jun 13, 2015 at 12:43 | answer | added | a00 | timeline score: 0 | |
| Jun 7, 2015 at 15:28 | comment | added | a00 | So I am basically saying you can take partial derivatives in any order. I now read that one can only switch around the order of partial derivatives in this way if the partial derivative(s) of Ψ are continuous. (mhhe.com/math/calc/smithminton2e/cd/folder_structure/text/… about 2/3rds the way down) So I guess it's often glossed over that wave functions are continuous when differentiated with respect to r,θ,φ. (They are, right?) | |
| Jun 6, 2015 at 13:11 | comment | added | a00 | Basically I think if you have two operators that depend on different variables in this way, if you expand out the expression for the two different order of operations (for example, (L^2)*(KE) and (KE)*(L^2)) basically you get a long sum of various products. But all these products can be rearranged to look like the other order of operation's products because "anything on the inside of a derivative of θ that depends only on φ or r can come out of the derivative", and similarly for derivatives of φ and r. | |
| Jun 6, 2015 at 13:07 | comment | added | a00 | He says "An operator can commute with another independent operator" by which I think he means that if one operator depends only on certain variables, and another operator depends only on different variables, then they commute. L^2 depends on θ,φ only and Kinetic Energy depends on r only, thus they commute. | |
| Jun 5, 2015 at 15:35 | comment | added | user46925 | qest 1: it's well detailled from page 13 last paragraph until the line preceding the conclusion in the middle of the next page ( impossible copy paste ) | |
| Jun 5, 2015 at 15:11 | history | edited | Kyle Kanos | CC BY-SA 3.0 |
Improved formatting
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| Jun 5, 2015 at 14:29 | review | First posts | |||
| Jun 5, 2015 at 14:33 | |||||
| Jun 5, 2015 at 14:28 | history | asked | a00 | CC BY-SA 3.0 |