The total energy of a particle-spring system in which theparticle moves with simple harmonic motion along theхахis isE =+2 m2where p, is the momentum of the quantum particle and kis the spring constant. (a) Using the uncertainty principle,show that this expression can also be written as+8p?(b) Show that the minimum energy of the harmonic oscil-lator iskE = K+ U=Aminm 4+

Given data The total energy of a particle is, Step 1 The uncertainty principle is, The total…

Answered: The total energy of a particle-spring…

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter40: Quantum Mechanics

Section: Chapter Questions

Problem 27P

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Similar questions

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.
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assume that an electron is moving along the x-axis and that you measure its speed to be 20.5*10^6m/s, which can be known with of precision of 0.50%. what is the minimum uncertainty (as allowed by the uncertainty principle in quantum theory )with which you can simultaneously measure the position of the electron along the x-axis?
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A quantum particle in an infinitely deep square well has a wave function that is given by ψ1(x) = √2/Lsin (πx/L)for 0 ≤ x ≤ L and is zero otherwise. (a) Determine the probability of finding the particle between x = 0 and x = 1/3L.(b) Use the result of this calculation and a symmetry argumentto find the probability of finding the particle between x = 1/3 L and x = 2/3 L. Do not re-evaluate the integral.
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A three-dimensional wave function of a particle is u(x)=c/r exp(-kr/i)calculate the probability currentdensity
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