PHYSICS F/SCI.+ENGR.,V.1 (CHAP.1-20)
5th Edition
ISBN: 9780134378053
Author: GIANCOLI
Publisher: RENT PEARS
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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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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.
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.
one-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.
Chapter 38 Solutions
PHYSICS F/SCI.+ENGR.,V.1 (CHAP.1-20)
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- A 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_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_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_forwardConsider a particle in an infinite square well where the length is a and the initial wave function is 0 < x < "/2 -{ Ax Ч(х, 0) А(а — х) "/2arrow_forwardChapter 39, Problem 015 An electron is trapped in a one-dimensional infinite potential well that is 150 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width dx = 5.0 pm centered at x = 56 pm? (Hint: The interval dx is so narrow that you can take the probability density to be constant within it.) Number Unitsarrow_forwardThe potential energy Uis zero in the interval 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_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_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_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_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_forwardFor a particle inside a box of finite potential well, the particle is most stable at what position of x? a) x > L b) x < 0 c) 0 < x < L d) Not stable in any statearrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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