1.) Solve the time-independent Schrödinger equation for piecewise constant potential:
Q: ) Separable solutions to the (time-dependent Schrödinger equation ) lead to stationary stats. b)…
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Q: Consider the 1-dimensional quantum harmonic oscillator of mass u. xeax*/½ is an eigenfunction of the…
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Q: mw?g2 Consider a one-dimensional anharmonic oscillator of the form: Ĥ + ax4 where 4) it is…
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Q: A particle of mass m is confined to a one-dimensional potential well. The potential energy U is 0…
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Q: 2. Example questions The energy levels of the Morse potential (in cm-¹) are given by, 2 = (v + ² ) h…
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Q: 1. Solve the Schrodinger equation for a particle of mass, m, in a box. The box is modeled as an…
A: 1) Given: Length of the box is L. Potential inside the box is V0 Calculation: The schematic diagram…
Q: 1. In a system of two conducting wires separated by a small distance L, an electron can potentially…
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Q: 5) Infinite potential wells, the bound and scattering states assume the same form, i.e. A sin(px) +…
A: The solution of this problem is following.
Q: 2. Consider two vectors, and v₂ which lie in the x-y plane of the Bloch sphere. Find the relative…
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Q: 15. For the wavefunction (x) location of the particle? = Nre 22, where is the most probable
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Q: 3. Use the recursion formula for the Hermite polynomial and the dipole moment series expansion to…
A: Hermit Polynomial Hr(y)12y4y2-28y3-12y16y4-48y2+1232y5-160y3+120y64y6-480y4+720y2-120 The Hermit…
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Q: 1. For the n 4 state of the finite square well potential, sketch: (a) the wave function (b) the…
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Q: Problem: In the problem of cubical potential box with rigid walls, we have: + m? +n? = 9, Write…
A: The given problem is a cubic potential box of length a (say). The potential function…
Q: Find the magnetic flux density due to the given current density everywhere: 4r² J(r) = Ho 0 5 1<r <2…
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Q: 4. Find the points of maximum and minimum probability density for the nth state of a particle in a…
A: For a 1-D box The wave function is, ψnx=2L sinnπxLProbability density, ρ=ψ*nψn =2L sinnπxL2L…
Q: iii) Consider a 2D square potential energy well with sides L (length) containing six electrons. The…
A: The electrons move in this two-dimensional box. The energy of these electrons can be calculated…
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- 7. Consider a particle in an infinite square well centered at x = 0 in one of its stationary states. For this problem, you may look up any integrals. Some useful ones are given in Harris. a) Compute (x) and (pr) for arbitrary n. Do this by direct computation but then describe how you could have found these results using symmetry (the symmetry can either be symmetry in the physical system, such as the shape of the wave function, or symmetry related to the expectation value integral, such as the shape of the integrand). b) Using your answer to part a), show that the uncertainty in the momentum is Apx nh for arbitrary n. Do this two ways: (i) first by using your answer to part a) and directly computating (p2) (via an integral) and (ii) by using your answer to part a) and relating (p2) to the kinetic energy operator. c) Show that the uncertainty principle holds for the ground state. 2L -18. In differential form, what is the kinetic energy operator equal to? Does this depend on the problem that you are solving in quantum mechanics? What is the eigenvalue spectrum for this operator?125. An attractive square well potential is 55 represented by -V for r a The scattering due to this potential in low energy limit is proportional to nth power of a. Here n is (1) 2 (2) 4 (3) 5 (4) 6