Assistance with last two questions Problem 1.14The one-dimensional harmonic oscillator has a potential V(x) = ka² /2. Wedenote the solutions of the associated Schrödinger equation as n(x), n =0, 1, 2, ... The energy of state „(x) isEn = hw(n + 1/2)(1.73)where w = VNow consider the two-dimensional harmonic oscillator which has a po-Vk/m.tentialkV (2, y) = (2² + y*).(1.74)1. Prove that Vmn(x, y)for the two-dimensional harmonic oscillator and find the correspondingenergy. [Hint: Group the second x-derivative term together with theka? /2 part of the potential, and do the same for y. Be sure fully toexploit the fact that m and n solve the Schrödinger equation for theone-dimensional harmonic oscillator.]Vm(x)vn(y) solves the Schrödinger equation2. What is the ground state energy for the two-dimensional harmonicocillator?3. What is the next lowest energy after the ground state, and which com-binations of (m, n) yield this energy?Problem 1.15

The one-dimensional harmonic oscillator has a potential V(x) = ka² /2. We Henote the solutions of the associated Schrödinger equation as (x), n = ), 1, 2, .... The energy of state Pn(x) is En = hw(n + 1/2) (1.73) vhere w = Vk/m. Now consider the two-dimensional harmonic oscillator which has a po- cential

The one-dimensional harmonic oscillator has a potential V(x) = ka² /2. We Henote the solutions of the associated Schrödinger equation as (x), n = ), 1, 2, .... The energy of state Pn(x) is En = hw(n + 1/2) (1.73) vhere w = Vk/m. Now consider the two-dimensional harmonic oscillator which has a po- cential

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter7: Tunneling Phenomena

Section: Chapter Questions

Problem 1P

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