Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
4th Edition
ISBN: 9780132273244
Author: Doug Giancoli
Publisher: PEARSON
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Chapter 38, Problem 13Q
To determine
The connection between the zero-point energy for a particle in rigid box and the uncertainty principle.
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What is the minimum Energy possessed by the particle in a box?
The general solution of the Schrodinger equation for a particle confined in
an infinite square-well potential (where V = 0) of width L is
w(x)= C sin kx + Dcos kx
V2mE
k
where C and D are constants, E is the energy of the particle and m is
the mass of the particle. Show that the energy E of the particle inside the
square-well potential is quantised.
Use the variational principle to obtain an upper limit to ground state energy of
a particle in one dimensional box.
Chapter 38 Solutions
Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
Ch. 38.3 - Prob. 1AECh. 38.8 - Prob. 1BECh. 38.8 - Prob. 1CECh. 38.9 - Prob. 1DECh. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Would it ever be possible to balance a very sharp...Ch. 38 - Prob. 6Q
Ch. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10QCh. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 17QCh. 38 - Prob. 18QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46GPCh. 38 - Prob. 47GPCh. 38 - Prob. 48GPCh. 38 - Prob. 49GPCh. 38 - Prob. 50GPCh. 38 - Prob. 51GPCh. 38 - Prob. 52GPCh. 38 - Prob. 53GPCh. 38 - Prob. 54GPCh. 38 - Prob. 55GPCh. 38 - Prob. 56GPCh. 38 - Prob. 57GPCh. 38 - Prob. 58GPCh. 38 - Prob. 59GP
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- Is it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?arrow_forwardCan a quantum particle 'escape' from an infinite potential well like that in a box? Why? Why not?arrow_forwardAn electron is trapped in an infinitely deep one- dimensional well of width 0.285 nm. Initially, the electron occupies the n = 4 state. (a) Suppose the electron jumps to the ground state with the accompanying emission of a photon. What is the energy of the photon? (b) Find the energies of other photons that might be emitted if the electron takes other paths between the n = 4 state and the ground state.arrow_forward
- For a particle in a one-dimensional box, calculate the probability of the particle to exists between the length of 0.30L and 0.70L if n = 5.arrow_forwardUsing the wave function and energy E, apply the Schrodinger equation for the particle within the box.arrow_forwardA quantum particle in an infinitely deep square well has a wave function given by ψ2(x) = √2/L sin (2πx/L)for 0 ≤ x ≤ L and zero otherwise. (a) Determine the expectation value of x. (b) Determine the probability of finding the particle near 1/2 L by calculating the probability that the particle lies in the range 0.490L ≤ x ≤ 0.510L. (c) What If? Determine the probability of finding the particle near 1/4L bycalculating the probability that the particle lies in the range 0.240L ≤ x ≤ 0.260L. (d) Argue that the result of part (a)does not contradict the results of parts (b) and (c).arrow_forward
- An electron is trapped in an infinitely deep potential well of width L = 1 nm. By solving the Schrödinger equation for this potential find the energy levels and calculate the wavelength of photon emitted from the transition E4 → E3.arrow_forwardA quantum mechanics problem Schrödinger's equation in the absence of a potential is ²=E, (1) 2m where his Planck's constant divided by 27, m is the mass, E is the energy, and is the wave- function. Consider a particle confined in a sphere of radius a. ("Confined" means that the wavefunction vanishes at r = a.) (a) Determine the possible values of the energy E, considering only states with no dependence on the azimuthal angle o. Also write down the corresponding states (i.e. wavefunctions). Note: Your answer will involve zeros of spherical Bessel functions. (b) Now consider only states with no dependence on the polar angle 0. Write down all values of the energy. You are given that the lowest energy state, which has energy E = Emin, is in this sector, i.e. has no angular dependence. What is Emin? Note: We are not dealing with superpositions in this question. We are interested in individual quantum states, which are specified by a value for I (which is called the angular momentum quantum…arrow_forwardAn electron trapped in a one-dimensional infinitely deep potential well with a width of 250 pm is excited from the first excited state to the third excited state. What energy must the electron acquire for this quantum jump to occur? The electron then emits a photon and transitions to the ground state. Determine the wavelength and momentum of the emitted photon.arrow_forward
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