EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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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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Students have asked these similar questions
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.
Prove that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a violation of the uncertainty principle Δpx Δx ≥ h/2.
What is the minimum Energy possessed by the particle in a box?
Chapter 38 Solutions
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- Use Heisenberg's uncertainty principle to estimate the ground state energy of a particle oscillating on an spring with angular frequency, =k/m, where k is the spring constant and m is the mass.arrow_forwardCan the magnitude of a wave function (*(x,t)(x,t)) be a negative number? Explain.arrow_forwardIs 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_forward
- If a classical harmonic oscillator can at rest, why can the quantum harmonic oscillator never be at rest? Does this violate Bohr 's correspondence principle?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
- An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).arrow_forwardUse the variational principle to obtain an upper limit to ground state energy of a particle in one dimensional box.arrow_forwardUsing the wave function and energy E, apply the Schrodinger equation for the particle within the box.arrow_forward
- A 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_forwardFor 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_forwardAn 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_forward
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