In solving the energy eigenproblem for the Quantum Harmonic Oscillator the final step is applying boundary condition to power series component of y^(5) = Ae 2 h (5) where h(5) = Σ 25' and leads to the recursion relationship; a+2= (2i+1-2k) (i+2)(i+1) a i=1 a. Using the above recursion, describe and show in words (and if applicable in equations) how the discrete energy E spectrum is found by applying the appropriate QM postulate(s). (Recall that K = from a needed substitution ħw early in the solution.) b. Write down the formula for the discrete energy spectrum, E, and show how it comes about. C. How does the discrete energy spectrum of the infinite square well come about? How is this process similar to that discussed above? How is it different?
In solving the energy eigenproblem for the Quantum Harmonic Oscillator the final step is applying boundary condition to power series component of y^(5) = Ae 2 h (5) where h(5) = Σ 25' and leads to the recursion relationship; a+2= (2i+1-2k) (i+2)(i+1) a i=1 a. Using the above recursion, describe and show in words (and if applicable in equations) how the discrete energy E spectrum is found by applying the appropriate QM postulate(s). (Recall that K = from a needed substitution ħw early in the solution.) b. Write down the formula for the discrete energy spectrum, E, and show how it comes about. C. How does the discrete energy spectrum of the infinite square well come about? How is this process similar to that discussed above? How is it different?
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Transcribed Image Text:In solving the energy eigenproblem for the Quantum Harmonic Oscillator the final step is applying boundary conditions
52
to power series component of 4 (5) = Ae 2 h(5) where h(5) = Σ a5 and leads to the recursion relationship;
24+2
i=1
(2i+1-2k)
(i+2)(i+1)
a
a.
Using the above recursion, describe and show in words (and if applicable in equations) how the discrete energy
E
spectrum is found by applying the appropriate QM postulate(s). (Recall that к = from a needed substitution
ħw
early in the solution.)
b.
Write down the formula for the discrete energy spectrum, Ę, and show how it comes about.
C.
How does the discrete energy spectrum of the infinite square well come about? How is this process similar to that
discussed above? How is it different?
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