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ChemistryPhysical ChemistryIndicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. (a) d d x cos 4 x (b) d 2 d x 2 cos 4 π x (c) p x ^ ( sin 2 π x 3 ) (d) x ^ ( 2 a sin 2 π x a ) (e) 3 ^ ( 4 ln x 2 ) , where 3 ^ = 3 × (f) d d θ sin π cos θ (g) d 2 d θ 2 sin π cos θ (h) d d π tan πStart your trial now! First week only $4.99!*arrow_forward*

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2nd Edition

Ball + 3 others

Publisher: Wadsworth Cengage Learning,

ISBN: 9781133958437

Chapter 10, Problem 10.11E

Textbook Problem

Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue.

**(a) **
**(b) **

**(c) **
** (d) **

**(e) **
** (f) **

**(g) **
**(h) **

Physical Chemistry

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Ch. 10 - Indicate which of these expressions yield an...Ch. 10 - Why is multiplying a function by a constant...Ch. 10 - Relating to the previous question, some texts...Ch. 10 - Using the original definition of the momentum...Ch. 10 - Under what conditions would the operator described...Ch. 10 - A particle on a ring has a wavefunction =12eim...Ch. 10 - Calculate the uncertainty in position, x, of a...Ch. 10 - For an atom of mercury, an electron in the 1s...Ch. 10 - Classically, a hydrogen atom behaves as if it were...Ch. 10 - The largest known atom, francium, has an atomic...Ch. 10 - How is the Bohr theory of the hydrogen atom...Ch. 10 - Though not strictly equivalent, there is a similar...Ch. 10 - The uncertainty principle is related to the order...Ch. 10 - What are the complex conjugates of the following...Ch. 10 - What are the complex conjugates of the following...Ch. 10 - For a particle in a state having the wavefunction...Ch. 10 - Repeat the above exercise for =2asin2xa How do...Ch. 10 - A particle on a ring has a wavefunction =eim,...Ch. 10 - A particle having mass m is described as having...Ch. 10 - Consider the same particle in the same box as in...Ch. 10 - Normalize the following wavefunctions over the...Ch. 10 - Normalize the following wavefunctions over the...Ch. 10 - A Gaussian function has the form eax2, where a is...Ch. 10 - Of the requirements of a proper wavefunction,...Ch. 10 - For an unbound or free particle having mass m in...Ch. 10 - Why does the Schrdinger equation have a specific...Ch. 10 - Explain the reason that the kinetic energy...Ch. 10 - Use the Schrdinger equation to evaluate the total...Ch. 10 - Evaluate the expression for the total energies for...Ch. 10 - Explain how the Hamiltonian operator is Hermitian....Ch. 10 - Verify that the following wavefunctions are indeed...Ch. 10 - In exercise 10.41a, the wavefunction is not...Ch. 10 - Verify the normalization constant on the...Ch. 10 - Verify that equation 10.11 satisfies the...Ch. 10 - Explain why n=0 is not allowed for a...Ch. 10 - Find the first three energies of a proton confined...Ch. 10 - Assume that an energy difference of 1.001032J is...Ch. 10 - What happens to the energy of a particle-in-a-box...Ch. 10 - Carotenes are molecules with alternating CC and...Ch. 10 - The electronic spectrum of the molecule butadiene,...Ch. 10 - How many nodes are there for the one-dimensional...Ch. 10 - Draw at least roughly plots for the first five...Ch. 10 - Show that the normalization constants for the...Ch. 10 - Evaluate the probability that an electron will...Ch. 10 - Determine the classical velocity of an electron in...Ch. 10 - An official baseball has a mass of 145g. a...Ch. 10 - Is the uncertainty principle consistent with our...Ch. 10 - From drawing of the probabilities of particles...Ch. 10 - What is the probability of finding a...Ch. 10 - Instead of x=0 to a, assume that the limits on the...Ch. 10 - In a plot of ||2, the maximum maxima in the plot...Ch. 10 - Explain how =2/asin(nx/a) isnt an eigenfunction of...Ch. 10 - Evaluate the average value of position, x, for the...Ch. 10 - The average value of radius in a circular system,...Ch. 10 - Evaluate the average value of position, x, for 2...Ch. 10 - Evaluate px, for 1 of a particle-in-a-box.Ch. 10 - If the operator x2=xx=x2, evaluate x2 for a...Ch. 10 - If the operator px2=pxpx=22x2, evaluate px2 for a...Ch. 10 - Evaluate E for 1 of a particle-in-a-box and show...Ch. 10 - Assume that for a particle on a ring the operator...Ch. 10 - Mathematically, the uncertainty A in some...Ch. 10 - Why do we define (1/X)(d2/dx2)X as (2mEx/2) and...Ch. 10 - What are the units on (1/X)(d2/dx2)X? Does this...Ch. 10 - Verify that the wavefunctions in equation 10.20...Ch. 10 - An electron is confined to a box of dimensions...Ch. 10 - a What is the ratio of energy levels having the...Ch. 10 - Consider a one-dimensional particle-in-a-box and a...Ch. 10 - Assume a particle is confined to a cubical box....Ch. 10 - Determine the degeneracies of all levels for a...Ch. 10 - From the expressions for the 1-D and 3-D...Ch. 10 - Determine the degeneracies for all energies of a...Ch. 10 - What are x,y, and z for 111 of a 3-D...Ch. 10 - What are x2, y2 and z2 for 111 of a 3-D...Ch. 10 - Show explicitly that 2 and 3 for the 1-D...Ch. 10 - Show explicitly that 111 and 112 for the 3-D...Ch. 10 - Why cant 0a1x2d for a 1-D particle-in-a-box be...Ch. 10 - Verify that 12d=21d=0 for the 1-D...Ch. 10 - Evaluate the following integrals of the...Ch. 10 - Substitute (x,t)=eiEt/(x) into the time-dependent...Ch. 10 - Write (x,t)=eiEt/(x) in terms of sine and cosine,...Ch. 10 - Evaluate |(x,t)|2. How does it compare to |(x)|2?Ch. 10 - Construct plots of the probabilities of the first...Ch. 10 - Numerically integrate the expression for the...Ch. 10 - Numerically integrate the 1-D particle-in-a-box...

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