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Fund Quantum Mechanics Lect &amp; HW Solutions 41

# Fund Quantum Mechanics Lect &amp; HW Solutions 41 - E n...

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3.5. A PARTICLE CONFINED INSIDE A PIPE 23 3.5.5 All solutions of the eigenvalue problem 3.5.5.1 Solution piped-a Question: Write down eigenfunction number 6. Answer: Substituting n = 6 in the generic expression for the eigenfunctions, ψ n = r 2 x sin p x x P you get ψ 6 = r 2 x sin p 6 π x x P 3.5.5.2 Solution piped-b Question: Write down eigenvalue number 6. Answer: Substituting n = 6 in the generic expression for the eigenvalues,
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Unformatted text preview: E n = n 2 ¯ h 2 π 2 2 mℓ 2 x you get E 6 = 36¯ h 2 π 2 2 mℓ 2 x 3.5.6 Discussion of the energy values 3.5.6.1 Solution pipee-a Question: Plug the mass of an electron, m = 9.109,38 10 − 31 kg, and the rough size of an hydrogen atom, call it ℓ x = 2 10 − 10 m, into the expression for the ground state kinetic energy...
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