Register

Adv. Query

Q&A (4902)

Reviews (206)

Open problems (47)
Meta (439)

Site Statistics

206 submissions , 164 unreviewed
5,106 questions , 2,251 unanswered
5,413 answers , 23,081 comments
1,470 users with positive rep
822 active unimported users
More ...

How symmetry is related to the degeneracy?

790 views

I have several questions about symmetry in quantum mechanics.

It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a symmetric group $G$, then the state space with the same energy eigenvalue will carry a representation of $G$. However, why this representation is usually irreducible?
Is it true that the representation of continuous symmetric group must be unitary and cannot be anti-unitary?
What is the difference between geometric symmetry and dynamical symmetry? By dynamical symmetry I mean for example the $\mathrm{SO}(4)$ symmetry of hydrogen. Some text refers dynamical symmetry to "internal" symmetry. How to state the definition of dynamical symmetry strictly?

This post imported from StackExchange Physics at 2014-08-11 14:59 (UCT), posted by SE-user Andrew

asked Mar 25, 2014 in Theoretical Physics by Andrew (135 points) [ no revision ]

Your comment on this question:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if my answer is selected or commented on:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverflo$\varnothing$
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).

Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

...