phy246s11_hw1sol

phy246s11_hw1sol - and(p t,h is an eigenfunction of H What...

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Physics 246 First Homework Set 1. S,rppose that the oscillator energy (i."., E _ A I p l" +B I r l" where A,B,o,,r are classical statistical mechanics. How would the distribution be affected by such a change? 2. Consider the system with Hamiltonian Due: January 28, 2011 the Hamiltonian) is replaced bY positive constants. Compute tr in Rayleigh.Jeans blackbody spectral H_ fif+v(") where . fo o V(*)- { 1oo r a) Show that where n - 1,,2,,,.. b) Calculate L'p c) Now consider ,[email protected])- and again compute Lp and 3:' A particle of mass m in an infinite square well proportional to sins ffi ,os ffi. a) What is the ,[email protected],t) for all t b)
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Unformatted text preview: (*), and (p) t ,[email protected]) is an eigenfunction of H. What is the eigenvalue? and L,r and compare with the uncertainty principle.- n Llz {., Atr. has a wave function at time t - $ \r :..,'.::,=t--.==. .'-''L--_K*@'_-?.=- L) L^ v- L-aye{t-/-\-,4l. - ' ,- t A, / Mfr,WYI J-,4 ^"IL L t-;l--r; -=4*iS-*+ € It /, TfK\ : 4-( ,l=--CA,- ? \rflt\h V \-'' l- ) 0(x 4 ..a.LC43o,3< T--+- Y;l\'/ | on" / 4r, ,l < fI= gra;i .t'* L* E.*st{i,^ry:; rsl k- gr,turt *o -***/*5+*+.o;5f .-- i I L,t-1 --.aL \ 'aa lrl%* -,------ = ! 14' 2^' .: i-Allw-:--- r-==-/-i. \ I- 1.5- r* i[;v-----{-iZ...
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