Modern Physics, 3rd Edition
3rd Edition
ISBN: 9780534493394
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 7, Problem 7P
To determine
The results for the transmission coefficient of a square barrier given in equation 7.9.
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Modern Physics, 3rd Edition
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- Consider a particle in a box of length L with one end coinciding with the origin. Consider the state with n=2. Compute the expectation value of position as a function of time as well as the extrema in the probability density as a function of time. Interpret.arrow_forwardConsider an infinite well, width L from x=-L/2 to x=+L/2. Now consider a trial wave-function for this potential, V(x) = 0 inside the well and infinite outside, that is of the form (z) = Az. Normalize this wave-function. Find , .arrow_forwardThe wavefunction for the particle in a one-dimensional infinite potential well is given by V(x, t) = VI 2 e-iEnt/h En n?n?h? sin 2mL2 with 0arrow_forwardPhysics Consider particles of mass "m" in an infinite square well (a box) of size "L". a. Write the wave function for a situation in which the particles are in a superposition of state "s" with energies E5, E6, E8 with probabilities P(E5) =P(E6) =1/4. b. Write explicitly the integral needed to calculate in order to find the average value of the position operator < X >. No need to calculate the integrals explicitly.arrow_forwardConsider a wave packet formed by using the wave function Ae -αIxI , where A is a constant to be determined by normalization. Normalize this wave function and find the probabilities of the particle being between 0 and 1/α, and between 1/α and 2/α.arrow_forwardShow that the probability of obtaining En for a particle in a box with the provided wave function (see first image) is given by the equation in the first image. Hint: The probability of obtaining the ground-state energy E1 is determined in Example 3.4, as shown in the second provided image.arrow_forwardNormalize the ground state wave function Ψ0 for the simple harmonic oscillator and find the expectation values (x) and (x 2).arrow_forwardAn atom with total energy 1.84 eV, in a region with no potential energy, is incident on a barrier with potential height 3.76 eV, and unknown thickness b. The probability that the atom passes through the barrier is 1.16%. If the thickness of the barrier is increased to 1.68b, what is the new probability of passing through the barrier (in %)?arrow_forwardOne-dimensional harmonic oscillators in equilibrium with a heat bath (a) Calculate the specific heat of the one-dimensional harmonic oscillator as a function of temperature. (b) Plot the T -dependence of the mean energy per particle E/N and the specific heat c. Show that E/N → kT at high temperatures for which kT > hw. This result corresponds to the classical limit and is shown to be an example of the equipartition theorem. In this limit the energy kT is large in comparison to ħw, the separation between energy levels. Hint: expand the exponential function 1 ē = ħw + eBhw (c) Show that at low temperatures for which ħw> kT , E/N = hw(+e-Bhw) What is the value of the heat capacity? Why is the latter so much smaller than it is in the high temperature limit? Why is this behavior different from that of a two-state system? (d) Verify that S →0 as T> O in agreement with the third law of thermodynamics, and that at high T,S> kN In(kT / hw).arrow_forwardA one -dimensional potential box of width a. O Show that the wavefunctron of a particle in the 2nd excited state and the wnve function f the particle in the 4th excited stat ar orthogonal.arrow_forwardAssume that you have a quantum mechanical observable N with eigenvalues Wi and corresponding eigenvectors |w;). Show that (n?) – (N)² where P(w;) is the probability of measuring the eigenvalue w; for some quantum state.arrow_forwardConsider a particle with energy E confined to a one-dimensional finite potential well of depth V0. Assuming that there is more than one allowed energy eigenstate with E < V0, do the following: a) Sketch the values of the wavefunction and the probability density for the first two states. b) Explain any features of your sketch that do not occur in classical physics.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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