Given that L* = L, ±iL, and L÷Ym (0, 6) = NYm±1 (0, 6), where N = h/(l+1±m) (t=m), show that, L* +L- L+ - L- (a) L, = and L, = 2i (b)L,Y10 (0,6) = c,Y11 (0,6) + Yi-1 (0,6) and find the constants c and ez. (c)Consider the function (0, 6), which has the expansion v (0,6) = E aYım (0.6), where ao = 2v2, az = a-1 = 2. m-1 Show that (0,6) is an eigenfunction of L, and find the corresponding eigenvalue.
Given that L* = L, ±iL, and L÷Ym (0, 6) = NYm±1 (0, 6), where N = h/(l+1±m) (t=m), show that, L* +L- L+ - L- (a) L, = and L, = 2i (b)L,Y10 (0,6) = c,Y11 (0,6) + Yi-1 (0,6) and find the constants c and ez. (c)Consider the function (0, 6), which has the expansion v (0,6) = E aYım (0.6), where ao = 2v2, az = a-1 = 2. m-1 Show that (0,6) is an eigenfunction of L, and find the corresponding eigenvalue.
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Transcribed Image Text:Given that
L* = L,±iL, and L+Ym (0, 0) = NËYm÷1 (0, 0),
where
N = h/(e+1+m) (l = m),
%3D
show that,
L+ + L-
L+ - L-
(a) L, =
and L,
2
2i
(b)L,Y10 (0, 6) = cY1 (0,6) + c„Y1-1 (0, 6) and find the constants e and c2.
(c)Consider the function (0,6), which has the expansion
1
v (0, 6) = E amYım (0,9), where ao = 2v2, a1 = a-1 = 2.
%3D
m=-1
Show that (0, 0) is an eigenfunction of L, and find the corresponding eigenvalue.
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