Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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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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Chapter 38 Solutions
Physics for Scientists and Engineers with Modern Physics
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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- 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_forwardIf 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_forward
- 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_forwardUse the variational principle to obtain an upper limit to ground state energy of a particle in one dimensional box.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_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_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_forward
- Using 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_forwardquestion:: show that the de broglie wavelength of a particle in a one dimesional box in the first excited state is equal to the length of the box.arrow_forward
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