. A quantum particle of mass m is in the potential given in the figure below. Between x = 0 and x = A the potential is zero and between x = A and x = B the potential is V₁. Outside this region (if x ≥ B or x ≤ 0), the potential is V2. Assume the particle has total energy E which is less than V₂ but greater than V₁, so classically the particle would be trapped between x = 0 and x = B. Energy A V₂ IN V₁ V=0 0 A V₂ B X (a) If this were a classical particle, would it have more kinetic energy (and therefore more momentum) in the region where the potential is zero or in the region where the potential is V₁? Explain. = (b) In the region where V = 0, the particle's wavefunction satisfies the time-independent Schrödinger equation, which is ²2(2) -ky(x) for some constant k₁. What is k₁ in terms of the values given in the problem? What is the corresponding wavelength A₁? d.x² (c) In the region where V = V₁, the particle's wavefunction satisfies the time-independent d²v(x) Schrödinger equation, which is -k(x) for a different constant k₂. What is k₂ dx² in terms of the values given in the problem? What is the corresponding wavelength λ₂?

. A quantum particle of mass m is in the potential given in the figure below. Between x = 0 and x = A the potential is zero and between x = A and x = B the potential is V₁. Outside this region (if x ≥ B or x ≤ 0), the potential is V2. Assume the particle has total energy E which is less than V₂ but greater than V₁, so classically the particle would be trapped between x = 0 and x = B. Energy A V₂ IN V₁ V=0 0 A V₂ B X (a) If this were a classical particle, would it have more kinetic energy (and therefore more momentum) in the region where the potential is zero or in the region where the potential is V₁? Explain. = (b) In the region where V = 0, the particle's wavefunction satisfies the time-independent Schrödinger equation, which is ²2(2) -ky(x) for some constant k₁. What is k₁ in terms of the values given in the problem? What is the corresponding wavelength A₁? d.x² (c) In the region where V = V₁, the particle's wavefunction satisfies the time-independent d²v(x) Schrödinger equation, which is -k(x) for a different constant k₂. What is k₂ dx² in terms of the values given in the problem? What is the corresponding wavelength λ₂?