Question 03:(10 points) Let the particle is confined in a finite potential well with energies E,...

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Question 03:(10 points) Let the particle is confined in a finite potential well with energies E₁, E₂ and E3, where E₁ < E₂ < E3. Answer: EB E2 Answer: EL V1 0 Figure (3) (a) (2 points) Rank from largest to smallest, the penetration depth for the eigenfunction correspondi the three energies in the classical forbidden region x < 0. Also provide mathematical justificatio for your answer V2 (b) (2 points) Compare the penetration depth for the eigenfunction corresponding to energy E, in the t forbidden regions (x < 0 and x > L). In which region it is penetrated more. Provide reason for you answer (c) Sketch the energy eigenfunctions for the three energies given on the figure. Use the energy horizontal lines as the horizontal axis for the corresponding curves. Note that it is scaled so your curves should have some quantitative features in them. You can sketch any possible energy eigenfunction for the given energies but make sure that the difference in the energies should be reflected in the profiles (shapes) of the corresponding eigenfunctions. Also be careful in sketching the part of the wavefunctions in classical forbidden regions considering the difference in the values of the potential there. Question 03:(10 points) Let the particle is confined in a finite potential well with energies E₁, E₂ and E3, where E₁ < E₂ < E3. Answer: EB E2 Answer: EL V1 0 Figure (3) (a) (2 points) Rank from largest to smallest, the penetration depth for the eigenfunction correspondi the three energies in the classical forbidden region x < 0. Also provide mathematical justificatio for your answer V2 (b) (2 points) Compare the penetration depth for the eigenfunction corresponding to energy E, in the t forbidden regions (x < 0 and x > L). In which region it is penetrated more. Provide reason for you answer (c) Sketch the energy eigenfunctions for the three energies given on the figure. Use the energy horizontal lines as the horizontal axis for the corresponding curves. Note that it is scaled so your curves should have some quantitative features in them. You can sketch any possible energy eigenfunction for the given energies but make sure that the difference in the energies should be reflected in the profiles (shapes) of the corresponding eigenfunctions. Also be careful in sketching the part of the wavefunctions in classical forbidden regions considering the difference in the values of the potential there.

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The finite potential well is an extension of the infinite potential well from the previous section T... View the full answer