A particle is confined to a two-dimensional box of length L and width 3L. The energy values are E = (Planck constant2ϝ2/2mL2)(nx2 + ny2/9). Find the two lowest degenerate levels.
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A particle is confined to a two-dimensional box of length L and width 3L. The energy...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
Sketch the energy level diagrams of the two different two-dimensional particle in-a-box systems given below.Include the lowest-five energy levels for each system. a.Square (i.e., a=b), degenerate energy levels b.Rectangle (i.e., a≠b) non-degenerate energy levels
P7D.6 Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction y,. (a) Without evaluating any integrals, explain why(- L/2. (b) Without evaluating any integrals, explain why (p)-0. (c) Derive an expression for ) (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En =n2h2 /8rnf and, because the potential energy is zero, all of this...
47 (a) A particle is confined inside a rectangular box with sides of length a, a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave functions have this energy b) Now assume the rectangular box has sides of length a, 2a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave functions have this energy.
What is the next level (above E = 50E0) of the two-dimensional
particle in a box in which the degeneracy is greater than 2?
image: http://puu.sh/bUs5o/109dd1ce84.png
problems 7 & 8
Problem 7: A particle confined in a rigid one-dimensional box of length 1 x 10-14m has an energy level ER = 32 MeV and an adjacent energy level En+1 = 50 MeV. 1 MeV = 1 x 106 eV (a) Determine the values of n and n + 1. Answer: n = 4 and n+1 = 5. (b) What is the wavelength of a photon emitted in the n+1 to n transition? Answer: X = 6.9...
1) Consider a particle with mass m confined to a one-dimensional infinite square well of length L. a) Using the time-independent Schrödinger equation, write down the wavefunction for the particle inside the well. b) Using the values of the wavefunction at the boundaries of the well, find the allowed values of the wavevector k. c) What are the allowed energy states En for the particle in this well? d) Normalize the wavefunction
Consider an electron confined to a two dimensional box with walls of length a and b. If this electron is represented by a standing waves with nodes along box's walls, calculate its energy.
Consider an electron confined to a two dimensional box with walls of length a and b. If this electron is represented by a standing waves with nodes along box's walls, calculate its energy.
The energy difference between two lowest energy levels for an alpha particle confined in a cube with sides of length 2 angstroms is DeltaE = 6.19×10^-22 J. At a temperature of 10K, can the particle be described classically or should it be treated using quantum mechanics?