A particle of mass m is constrained to move between two concentric impermeable spheres of radii r = a and r = b. There is no other potential. Find the ground state cnergy and norinalized wave function.
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- When a particle of energy E approaches a potential barrier of height V0, where E >> V0, show that the refl ection coeffcient is about {[V0 sin(kL)]/2E} 2Consider an electron in a one-dimensional, infinitely-deep, square potential well of width d. The electron is in the ground state. (a) Sketch the wavefunction for the electron. Clearly indicate the position of the walls of the potential well on your sketch. (b) Briefly explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.(b) Suppose a particle trapped in an one-dimensional box of width a with infinitely hard walls. Derive the normalized wave function from the solution of wave function? Find the probability of particle that can be found between 0.4a and 0.5a for the first excited state.
- A particle with mass m is in the state .2 mx +iat 2h Y(x,t) = Ae where A and a are positive real constants. Calculate the expectation values of (x).Find the lowest energy of an electron confined to move in a three dimensional potential box of length 0.48 Å.A particle with a width and an infinite one-dimensional potential is A perturbation of (V0 = constant) takes effect. Energy value with the first-order approach find.
- Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3A particle is trappend in a one-dimensional well. Two of its wavefunctions are shown below. (a) Identify wether the well is finite or infinite. (b) Identify the quantum number n associated with each wavefunction; (c) Overlay a sketch of the probability density for each wavefunction. n = n =Find the ground-state energy and wave function of a system of N identical non-interacting particles confined in a one-dimensional infinity well when the particles are (a) bosons and (b) fermions with spin 1/2
- The curve in the attached figure is alleged to be the wave function for the fifth energy level for a particle confied in the one-dimensional potential energy well shown. Quantitately prove which aspects of the wave function are correct, as well as which are not correct.Let 12.0-eV electrons approach a potential barrier of height 4.2 eV. (a) For what barrier thickness is there no refl ection? (b) For what barrier thickness is the refl ection a maximum?