Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 35, Problem 7P
To determine
The verificationthat normalization constant in the ground state is
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The wave function of the particle lies in which region?
a) x > 0
b) x < 0
c) 0 < X < L
d) x > L
Show that normalizing the particle-in-a-box wave function ψ_n (x)=A sin(nπx/L) gives A=√(2/L).
Calculate the transmission probability for quantum-mechanical tunneling in each of the following cases. (a) An electron with an energy deficit of U - E= 0.010 0 eV is incident on a square barrier of width L = 0.100 nm. (b) An electron with an energy deficit of 1.00 eV is incident on the same barrier. (c) An alpha particle (mass 6.64 × 10-27 kg) with an energy deficit of 1.00 MeV is incident on a square barrier of width 1.00 fm. (d) An 8.00-kg bowling ball withan energy deficit of 1.00 J is incident on a square barrier of width 2.00 cm.
Chapter 35 Solutions
Physics for Scientists and Engineers
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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- If STM is to detect surface features with local heights of about 0.0200 nm, what percent change in tunneling-electron current must the STM electronics be able to detect? Assume that the tunneling-electron current has characteristics given in the preceding problem.arrow_forwardShow that the wave function in (a) Equation 7.68 satisfies Equation 7.61, and (b) Equation 7.69 satisfies Equation 7.63.arrow_forwardThe normalization condition for a wavefunction Ψ(x, t) is given by � ∞ −∞ Ψ∗(x, t)Ψ(x, t)dx = 1. This necessarily means that the LHS has to be independent of time. Show that this is indeed the casearrow_forward
- The distance (spacing) between the energy levels of a harmonic oscillator is: a. Decreasing with n b. 2 c. constant d. Increasing with n I will rate accordingly. Donarrow_forwardFor a properly normalized wavefunction, determine the value of the integral of Ψ(x)Ψ*(x) (or Psi squared) from x = -infinity to +infinity 0 infinity -1 1 None of the abovearrow_forwardQ 3: Two people measure a wave of a particle passing from a point in front of them and their measurements are as follows: First person: W, (x,t) = Acos(5x — 3t) Second person: W,(x,t) = Acos(5.1x — 3.2t) 1 Find the wave packet consisting of these two waves in its simplest form. 2 2-If you know that at time t = 0.1s in position x = 1m, The wave packet was ¥(x.t) = 7.9726375772 what is the value of the constant Aarrow_forward
- Consider scattering with electrons of 54 eV on a crystal with planes separated by 0.22 nm. How many diffraction peaks should be expected? Justify your answerarrow_forward(a) Find the excitation energy from the ground level to the third excited level for an electron confined to a box of width 0.360 nm. (b) The electron makes a transition from the n = 1 to n = 4 level by absorbing a photon. Calculate the wavelength of this photon.arrow_forwardIn a Davisson-Germer experiment, electrons with a speed of 6.5 × 106 m/s exhibit third-order ( n = 3) constructive interference for a crystal with unknown plane separation, d. Given an angle of incidence of θ = 45°, compute the value for d. Compare the de Broglie wavelength to electromagnetic radiation with the same wavelength. (Recall that the mass of the electron is 9.11 × 10-31 kg.)arrow_forward
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