EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 38, Problem 17Q
To determine
The change in particle’s ground state energy and wave function if potential wells become finite and decreases and drops to zero.
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16
An electron with energy E= +4.80 eV is put in an infinite potential well with U(x) =infinity for x<0 and x>L. Of course, U(x) = 0 for 0<x<L. Find the largest amount of time that the electron can exist outside the box. Draw and Label a figure.
Question A6
Consider an infinite square well with V = 0 in the interval -L/2 < x < L/2, and V → ∞
everywhere else. A particle of mass m is in the groundstate of this system, and is known to have
a wavefunction and energy given by
TX
√ =
COS
and
E =
π²h²
2mL²
The system is then perturbed so that its potential takes the constant value V
Chapter 38 Solutions
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- 24. Consider a modified box potential with V(x) = V₁x, Vi(ar), x a Use the orthogonal trial function = c₁f₁+c₂f₂ with f₁ = √√sin (H) and f2 = √√ √√sin sin (2) to determine the upper bound to ground state energy.arrow_forwardExample 6. A particle of mass 'm’ is moving in a one-dimensional box defined by the potential V = 0, 0sxsa and V = o othcrwise. Estimate the ground state energy using the trial function y (x) = Ax(a-x), OSxarrow_forwardone-dimensional A one-particle, system has the potential energy function V = V₁ for 0 ≤ x ≤ 1 and V = ∞ elsewhere (where Vo is a constant). a) Use the variation function = sin() for 0 ≤ x ≤ 1 and = 0 elsewhere to estimate the ground-state energy of this system. b) Calculate the % relative error.arrow_forwardA particle is trapped in an infinite one-dimensional well of width L. If the particle is in its ground state, evaluate the probability to find the particle (a) between x = x = L/3; (b) between x = L/3 and x = x = 2L/3 and x = L. O and 2L/3; (c) between %3Darrow_forwardThe potential energy Uis zero in the interval 0arrow_forwardGiven: For sake of simplicity, let us consider a particle with mass, m, in one dimension trapped in an infinite square well potential. The bottom of the potential well has zero potential energy, and the particle is known to be confined between 0arrow_forward7. Schrödinger's equation A particle of mass m moves under the influence of a potential given by the equation U(x) -W 0 where a is half the width of the potential well. Consider that the energy of the particle. E, is such that -W a = = 2m(E + W) h² 2mE h²arrow_forwardB6arrow_forwardAn electron of mass m is confined in a one-dimensional potential bor between x = 0 to x = a. Find the expectation value of the position coordinate x of the particle in the n =1 state. Estimate the result for higher energy state n.arrow_forwardThe ground state energy of a particle in a one-dimensional infinite potential well of width 1.5 nm is 20 eV. The ground state energy of the same particle in a one-dimensional finite potential well with U0 = 0 in the region 0 < x < 1.5 nm, and U0 = 50 eV everywhere else, would be greater than 50 eV. less than 20 eV. greater than 20 eV, but less than 50 eV. equal to 50 eV. equal to 20 eV.arrow_forwardThe energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n = quantum number):arrow_forwarda. Consider a particle in a box with length L. Normalize the wave function: (x) = x(L – x) b. Consider a particle in a box of length L= 1 for the n= 2 state. Determine which of the two wave functions is normalized: v(x) = sin (27x) %3|arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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