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 Advanced Thermodynamics Advanced Thermodynamics Physics Help Forum Jan 20th 2010, 08:58 AM #1 Junior Member   Join Date: Jan 2010 Posts: 1 particle degeneracy I'm trying to calculate the degeneracy of the first few levels of a free particle confined to a cube of length a. To start, I think I need to consider the energy states of a particle in a 3-D infinite well (the picture attachment). But I'm not sure where I'm supposed to go from there... Attached Images    Jan 20th 2010, 09:50 AM #2 Junior Member   Join Date: Jan 2010 Posts: 9 The eigenfunctions are sine waves of the right wavelength. The energy operator is essentially a second derivative. The directions x,y,z act independently, so you will have a complete eigenfunction that's a product of an X part, a Y part and a Z part. To see the degeneracy, just find out how many ways there are to write a particular energy. For example: Energy 1 = 1^2+0+0 (x contribution =1, y=0,z=0) 1 = 0 + 1 + 0 1 = 0 + 0 + 1, so degeneracy = 3 here. For higher values, there may be other ways to write the energy, for instance: 2 = 1 + 1 + 0 ( & permutations) 3 = 1 + 1 + 1 (only 1 way ) etc.  Tags degeneracy, particle Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post simong Philosophy of Physics 28 Jun 12th 2014 09:27 AM ant17 Nuclear and Particle Physics 1 Nov 26th 2013 12:01 PM HoneyPi Equilibrium and Elasticity 1 Oct 8th 2009 02:52 AM ibeh Ngozi Chinomso Nuclear and Particle Physics 2 Sep 3rd 2009 08:10 AM esorolla Quantum Physics 1 Aug 12th 2009 09:51 PM