Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 7CQ
To determine
The physics accounts for the difference.
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A particle of mass m is moving in an infinite 1D quantum well of width L. y,(x) = J? sinx.
sin nAx
L
(a)
How much energy must be given to the particle so it can transition from the ground state
to the second excited state?
(b)
If the particle is in the first excited state, what is the probability of finding the particle
between x = and x = ;?
2.
What do we need to do to average over Θ and ф to get the probability that the electron is inside a shell of radius r and thickness dr?
The ground state wave function for the quantum mechanical simple harmonic oscillator is of
the form,
y(x)= A,e-**
mo,
a =
where A, is the normalization factor and a is a constant that depends on the mass and
classical frequency of the oscillator. Find the normalization factor in terms of the mass and
classical frequency w, The following definite integral should be helpful:
1
2a
Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
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Similar questions
- Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).arrow_forward. An electron in a long organic molecule used in a dye laser behave approximately like a particle in a box with width 4.18 nm. (a) What is the λ of the proton emitted when the electron undergoes a transition from the first excited level to the ground level. (b) What is the λ of the proton emitted when electron undergoes a transition from the second excited level to the first excited level?arrow_forwardSuppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?arrow_forward
- Verify that given by Equation 7.57 is a solution of Schrödinger's equation for the quantum harmonic oscillator. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,...arrow_forwardCheck Your Understanding Which of the following wave functions is valid wave-function solution for Schr0dinger’s equation?arrow_forwardCheck Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in the region O and L. One possible wave function is (x,t)={AeiEt/hsinxL, when 0xL otherwise Determine the normalization constant.arrow_forward
- The wave function is evaluated at rectangular coordinates (x. y, z) = (2, 1, 1) in arbitrary units. What are the spherical coordinates of this position?arrow_forwardWhat is the ground state energy (in eV) of a proton confined to a one-dimensional box the size of the uranium nucleus that has a radius of approximately 15.0 fm?arrow_forwardA particle of massm in a harmonic oscillator potential with angular frequency w is in the state (1 + {t)쭈 What is (p?) for this particle? mhw 2 O 6mħw O 3mhwarrow_forward
- Q#07. Consider the following three wave functions: 41y) = A,e¬y² P2v) = Aze-&²/2) 3(v) = A3 (e¯y² + ye-*/2) where A1, 42, and A3 are normalization constants. (a) Find the constants A1, A2, and A3 so that 2, P1, and wz are normalized. (b) Find the probability that each one of the states will be in the interval -1< y< 1.arrow_forwardConsider a particle of mass m, located in a potential energy well.one-dimensional (box) with infinite height walls. The wave function that describes this system is:Ψn(x) = K sin (nπx /L), for 0 ≤ x ≤ LΨn(x) = 0 for any other value.K is a constant and n = 1,2,3,... Determine K*K = │K│2arrow_forwardWhat is the probability of the particle that in the box with a length of 2 nm is between x = 0.2 and x = 1.0 nm? Ѱ=√(2/L)*sin(nπx/L)arrow_forward
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