Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 6, Problem 21P
To determine
The sketch of wavelength and the probability density for
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A particle of mass m is confined to a one-dimensional (1D) infinite well (i.e., a 1D box)
of width 6 m.
The potential energy is given by
(0 6m)
The particle is in the n=5 quantum state. What is the lowest positive value of x (in m)
such that the particle has zero probability of being found at x?
A particle is in the ground state of an infinite square-well potential. The
probability of finding the particle in Ax = 0.01L at x = L/4 is
A particle of mass m is trapped in a three-dimensional rectangular potential well with sides of length L, L/ √2, and 2L. Inside the box V = 0, outside V = ∞. Assume that Ψ = Asin (k1x) sin (k2y) sin (k3z) inside the well. Substitute this wave function into the Schrödinger equation and apply appropriate boundary conditions to find the allowed energy levels. Find the energy of the ground state and first four excited levels. Which of these levels are degenerate?
Chapter 6 Solutions
Modern Physics
Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.5 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.8 - Prob. 6ECh. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5Q
Ch. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 21PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 37PCh. 6 - Prob. 38P
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- A particle of mass m, which moves freely inside an infinite potential well of length a, is initially in the state y(x,0)=√√3/5a sin (3xx/a)+ (1/√5a) sin (5mx/a). (a) Find y (x, t) at any later time t. Calculate the pr Lility density of thouarrow_forwardThe wavefunction for a particle in a box in a three -dimensional potential energy well isΨ (x,yz) = A sin (nxπx/a) (nyπy/b) (nzπz/c)Determine the eigenvalue for the energy.arrow_forwardUsing the properly normalized wave functions for a particle in an infinite one-dimensional well of width L for the n = 1 state, find the probability that the particle will be found in the region of L/3 to L/2arrow_forward
- Consider a particle in a box of length L= 1 for the n= 2 state. The wave function is defined as: (x) = sin (27x) %3| Normalize the wave function.arrow_forwardAn electron is trapped in a one-dimensional infinite potential well that is 460 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width δx = 5.0 pm centered at x = 300 pm? (Hint: The interval δx is so narrow that you can take the probability density to be constant within it.)arrow_forwardAssume that an electron is confined in a one-dimensional quantum well with infinite walls, draw the wave functions for the first 3 levels, ψ1, ψ2, ψ3. Also, show the probability density functions corresponding to these three levels?arrow_forward
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