Please answer d,e and f A quantum particle of mass m is in the potential given in the figure below. Between x = 0and x = A the potential is zero and between x = A and x = B the potential is V₁. Outsidethis region (if x ≥ B or a ≤ 0), the potential is V₂. Assume the particle has total energy Ewhich is less than V₂ but greater than V₁, so classically the particle would be trapped betweenx = 0 and x = B.V₂Energy A0V=0V₁A=V₂BX(a) If this were a classical particle, would it have more kinetic energy (and therefore moremomentum) in the region where the potential is zero or in the region where the potentialis V₁? Explain.(b) In the region where V = 0, the particle's wavefunction satisfies the time-independentd²v(x)Schrödinger equation, which is-k(r) for some constant k₁. What is k₁ indr²terms of the values given in the problem? What is the corresponding wavelength A₁?(c) In the region where V = V₁, the particle's wavefunction satisfies the time-independentSchrödinger equation, which is ²) = -ky(r) for a different constant k₂. What is k₂in terms of the values given in the problem? What is the corresponding wavelength X₂?(d) Is A2 larger or smaller than A₁? Is the de Broglie momentum of the particle larger inthe region where the potential is zero or larger where the potential is V₁? How does thiscompare to the classical case (part a)?(e) In the regions where the potential is V₂, the particle's wavefunction satisfies the time-independent Schrödinger equation, which is d²v(x) = +ay(x) some constant a₁. Whatis a₁ in terms of the values given in the problem?dr²(f) Sketch a possible wavefunction for a quantum particle moving in this potential as afunction of x (it doesn't matter which mode, just pick one!). For the oscillating part,make sure to show how the wavelength changes in different regions.

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