Question 1

A particle is in a three-dimensional box with L3 = L2 = 3L1. The lowest energy level is

Accepted Answer

A)  zero 
B)  1.22E0  
C)  1.56E0  
D)  1.67E0  
E)  1.94E0  
A)  zero 
B)  1.22E0  
C)  1.56E0  
D)  1.67E0  
E)  1.94E0

Question 2

Suppose the natural frequency of oscillation for H2 is $\backsim$1012 Hz, the effective spring constant between the two H atoms is of the order

Accepted Answer

A)  10-1 N/m 
B)  10-3 N/m 
C)  10-5 N/m 
D)  10-7 N/m 
E)  10-9 N/m 
A)  10-1 N/m 
B)  10-3 N/m 
C)  10-5 N/m 
D)  10-7 N/m 
E)  10-9 N/m

Question 3

An electron is confined in a two-dimensional box where U(x,y) = 0 for x = 0 to L, and y = 0 to 3L, and U(x,y) = infinity outside these boundaries. If L = 0.5 nm then calculate the energy of the first doubly degenerate levels.

Accepted Answer

A)  9.9 eV 
B)  11.0 eV 
C)  8.5 eV 
D)  7.7 eV 
E)  6.2 eV 
A)  9.9 eV 
B)  11.0 eV 
C)  8.5 eV 
D)  7.7 eV 
E)  6.2 eV

Question 4

The potential energy function shown in the above figure

Accepted Answer

A)  applies to any system undergoing small oscillations about a position of stable equilibrium. 
B)  shows the classical turning points ±A. 
C)  tells that where -A 2. 
E)  All of these are correct. 
A)  applies to any system undergoing small oscillations about a position of stable equilibrium. 
B)  shows the classical turning points ±A. 
C)  tells that where -A 2. 
E)  All of these are correct.

Question 5

Which of the following statements is true?

Accepted Answer

A)  A particle that is confined to some region of space can have zero energy. 
B)  All phenomena in nature are adequately described by classical wave theory. 
C)  The Schrödinger equation can be derived from Newton's laws of motion. 
D)  The penetration of a barrier by a wave has physical significance. 
E)  None of these is true. 
A)  A particle that is confined to some region of space can have zero energy. 
B)  All phenomena in nature are adequately described by classical wave theory. 
C)  The Schrödinger equation can be derived from Newton's laws of motion. 
D)  The penetration of a barrier by a wave has physical significance. 
E)  None of these is true.

Question 6

When a particle of energy E encounters the step function shown in the figure,

Accepted Answer

A)  the classical and quantum-mechanical descriptions are in agreement provided
E 0. 
B)  the wave function does not go to zero at x = 0 but rather decays exponentially. 
C)  the particle will sometimes be transmitted and sometimes reflected if E > U0. 
D)  the wavelength of the particle changes abruptly at x = 0 if E > U0. 
E)  All of these are true. 
A)  the classical and quantum-mechanical descriptions are in agreement provided
E 0. 
B)  the wave function does not go to zero at x = 0 but rather decays exponentially. 
C)  the particle will sometimes be transmitted and sometimes reflected if E > U0. 
D)  the wavelength of the particle changes abruptly at x = 0 if E > U0. 
E)  All of these are true.

Question 7

The energy in the first excited state of an electron confined to a one-dimensional box of length L = 0.3 nm is

Accepted Answer

A)  9.40 eV 
B)  12.3 eV 
C)  16.7 eV 
D)  24.2 eV 
E)  37.6 eV 
A)  9.40 eV 
B)  12.3 eV 
C)  16.7 eV 
D)  24.2 eV 
E)  37.6 eV

Question 8

The curve that best represents the ground-state energy for a finite square well is

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 9

A particle is in a three-dimensional box with L3 = L2 = 3L1. The energy level E1,1,2 is

Accepted Answer

A)  zero 
B)  1.22E0  
C)  1.56E0  
D)  1.67E0  
E)  1.94E0  
A)  zero 
B)  1.22E0  
C)  1.56E0  
D)  1.67E0  
E)  1.94E0

Question 10

Match each of the wave function on the left for a particle in a finite square well with the corresponding probability distributions on the right, in the order (a), (b), and (c).
(a)   (I)   (b)   (II)   (c)   (III)

Accepted Answer

A)  (II) (I) (III) 
B)  (II) (III) (I) 
C)  (III) (I) (II) 
D)  (III) (II) (I) 
E)  (I) (III) (II) 
A)  (II) (I) (III) 
B)  (II) (III) (I) 
C)  (III) (I) (II) 
D)  (III) (II) (I) 
E)  (I) (III) (II)

Question 11

The probability of penetration of a rectangular barrier ________ with the barrier thickness.

Accepted Answer

A)  increases linearly 
B)  decreases exponentially 
C)  decreases linearly 
D)  increases exponentially 
E)  decreases as a damped sinusoid 
A)  increases linearly 
B)  decreases exponentially 
C)  decreases linearly 
D)  increases exponentially 
E)  decreases as a damped sinusoid

Question 12

A particle of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.4E0. The probability that the particle will be reflected is

Accepted Answer

A)  0.316% 
B)  0.789% 
C)  1.61% 
D)  3.56% 
E)  4.12% 
A)  0.316% 
B)  0.789% 
C)  1.61% 
D)  3.56% 
E)  4.12%

Question 13

The time-independent Schrödinger equation is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

The energy in the ground state of an electron confined to a one-dimensional box of length L = 0.2 nm is

Accepted Answer

A)  1.88 eV 
B)  4.47 eV 
C)  6.25 eV 
D)  9.40 eV 
E)  None of these is correct. 
A)  1.88 eV 
B)  4.47 eV 
C)  6.25 eV 
D)  9.40 eV 
E)  None of these is correct.

Question 15

Particles that have symmetric wave functions and are not subject to the Pauli exclusion principle are called

Accepted Answer

A)  quarks 
B)  leptons 
C)  fermions 
D)  bosons 
E)  None of these is correct. 
A)  quarks 
B)  leptons 
C)  fermions 
D)  bosons 
E)  None of these is correct.

Question 16

A particle of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U0. What is the ratio of E0/U0 so that the reflection co-efficient is 75%? (Assume E0 is much less than the rest mass energy of the particle.)

Accepted Answer

A)  1.250 
B)  0.7500 
C)  1.778 
D)  1.005 
E)  1.063 
A)  1.250 
B)  0.7500 
C)  1.778 
D)  1.005 
E)  1.063

Question 17

In three dimensions, the Schrödinger equation for the infinite square-well potential

Accepted Answer

A)  has a solution of the form $\Psi$(x,y,z) = A sin k1x sin k2y sin k3z, where the k's are wave numbers and the constant A is determined by normalization. 
B)  predicts energy states described by   . 
C)  predicts energies and wave functions that are characterized by three quantum numbers. 
D)  allows multiple quantum states corresponding to the same energy level. 
E)  All of these are true. 
A)  has a solution of the form $\Psi$(x,y,z) = A sin k1x sin k2y sin k3z, where the k's are wave numbers and the constant A is determined by normalization. 
B)  predicts energy states described by   . 
C)  predicts energies and wave functions that are characterized by three quantum numbers. 
D)  allows multiple quantum states corresponding to the same energy level. 
E)  All of these are true.

Question 18

Suppose the natural frequency of oscillation for H2 is $\backsim$1012 Hz and the amplitude of oscillation is $\backsim$10-12 m, the total energy of the harmonic oscillator is of the order

Accepted Answer

A)  10-20 J 
B)  10-22 J 
C)  10-24 J 
D)  10-26  J 
E)  10-28 J 
A)  10-20 J 
B)  10-22 J 
C)  10-24 J 
D)  10-26  J 
E)  10-28 J

Question 19

The graph that shows the third state for a particle in a finite square well is

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  None of these is correct. 
A)  1 
B)  2 
C)  3 
D)  4 
E)  None of these is correct.

Question 20

The graph that represents the potential energy for a one-dimensional box from x = 0 to x = L is

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Exam 15: Applications of the Schrodinger Equation

A particle is in a three-dimensional box with L3 = L2 = 3L1. The lowest energy level is

Suppose the natural frequency of oscillation for H2 is ∽\backsim∽ 1012 Hz, the effective spring constant between the two H atoms is of the order

An electron is confined in a two-dimensional box where U(x,y) = 0 for x = 0 to L, and y = 0 to 3L, and U(x,y) = infinity outside these boundaries. If L = 0.5 nm then calculate the energy of the first doubly degenerate levels.

The potential energy function shown in the above figure

Which of the following statements is true?

When a particle of energy E encounters the step function shown in the figure,

The energy in the first excited state of an electron confined to a one-dimensional box of length L = 0.3 nm is

The curve that best represents the ground-state energy for a finite square well is

A particle is in a three-dimensional box with L3 = L2 = 3L1. The energy level E1,1,2 is

Match each of the wave function on the left for a particle in a finite square well with the corresponding probability distributions on the right, in the order (a), (b), and (c). (a) (I) (b) (II) (c) (III)

The probability of penetration of a rectangular barrier ________ with the barrier thickness.

A particle of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.4E0. The probability that the particle will be reflected is

The time-independent Schrödinger equation is

The energy in the ground state of an electron confined to a one-dimensional box of length L = 0.2 nm is

Particles that have symmetric wave functions and are not subject to the Pauli exclusion principle are called

A particle of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U0. What is the ratio of E0/U0 so that the reflection co-efficient is 75%? (Assume E0 is much less than the rest mass energy of the particle.)

In three dimensions, the Schrödinger equation for the infinite square-well potential

Suppose the natural frequency of oscillation for H2 is ∽\backsim∽ 1012 Hz and the amplitude of oscillation is ∽\backsim∽ 10-12 m, the total energy of the harmonic oscillator is of the order

The graph that shows the third state for a particle in a finite square well is

The graph that represents the potential energy for a one-dimensional box from x = 0 to x = L is

The Electric Field I: Discrete Charge Distributions

The Electric Field II: Continuous Charge Distributions

Electric Potential

Capacitance

Electric Current and Direct-Current Circuits

The Magnetic Field

Sources of the Magnetic Field

Magnetic Induction

Alternating-Current Circuits

Maxwells Equations and Electromagnetic Waves

Properties of Light

Optical Images

Interference and Diffraction

Wave Particle Duality and Quantum Physics

Atoms

Molecules

Solids and the Theory of Conduction

Relativity

Nuclear Physics

Elementary Particles and the Beginning of the Universe

Filters

A particle is in a three-dimensional box with L₃ = L₂ = 3L₁. The lowest energy level is

Suppose the natural frequency of oscillation for H₂ is $\backsim$ 10¹² Hz, the effective spring constant between the two H atoms is of the order

A particle is in a three-dimensional box with L₃ = L₂ = 3L₁. The energy level E_1,1,2 is

A particle of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.4E₀. The probability that the particle will be reflected is

A particle of kinetic energy E₀ traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U₀. What is the ratio of E₀/U₀ so that the reflection co-efficient is 75%? (Assume E₀ is much less than the rest mass energy of the particle.)

Suppose the natural frequency of oscillation for H₂ is $\backsim$ 10¹² Hz and the amplitude of oscillation is $\backsim$ 10^-1² m, the total energy of the harmonic oscillator is of the order