Question 1

The wave function shown in the figure represents the n = _______ energy state of the harmonic oscillator.

Accepted Answer

A)   0
B)   1
C)   2
D)   3
E)   4 C

Question 2

An electron confined to a one-dimensional box of length L = 0.2 nm makes a transition from state n = 4 to state n = 3. The wavelength of the photon emitted is

Accepted Answer

A)   19.0 nm
B)   17.2 nm
C)   14.6 nm
D)   12.5 nm
E)   10.8 nm A

Question 3

The wave function for the energy level in a cubical box of side L that corresponds to the quantum numbers 1, 2, and 3 is

Accepted Answer

A)    Ψ\PsiΨ 1,2,3 = A sin(  π\piπ x/L)  sin(2  π\piπ x/L)  sin(  π\piπ x/L) 
B)    Ψ\PsiΨ 1,2,3 = A sin(  π\piπ x/L)  sin(  π\piπ x/L)  sin(3  π\piπ x/L) 
C)    Ψ\PsiΨ 1,2,3 = sin(2  π\piπ x/L)  sin(3  π\piπ x/L) 
D)    Ψ\PsiΨ 1,2,3 = A sin(  π\piπ x/L)  sin(2  π\piπ x/L)  sin(3  π\piπ x/L) 
E)    Ψ\PsiΨ 1,2,3 = 2A sin(  π\piπ x/L)  sin(2  π\piπ x/L)  sin(3  π\piπ x/L)   D

Question 4

A particle is confined in a three-dimensional box with L1 = L2 = 3L3. The quantum numbers for the second excited state are

Accepted Answer

A)   (1,1,2)  and (1,2,1) 
B)   (1,2,1)  and (2,1,1) 
C)   (2,2,1)  and (2,1,2) 
D)   (1,2,2)  and (2,1,2) 
E)   (2,2,1)  and (1,2,2)

Question 5

Particles that have antisymmetric wave functions and are described by the Pauli exclusion principle are called

Accepted Answer

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

Question 6

The graph that shows the second 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.

Question 7

The wave function shown in the figure represents the n = _______ energy state of the harmonic oscillator.

Accepted Answer

A)   0
B)   1
C)   2
D)   3
E)   4

Question 8

An electron of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.5E0. The ratio of the wavelength of the transmitted wave to the incident wave is

Accepted Answer

A)   2
B)   1
C)   0.5
D)   0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.5E0. The ratio of the wavelength of the transmitted wave to the incident wave is 
A)   2 
B)   1 
C)   0.5 
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >
E)   0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.5E0. The ratio of the wavelength of the transmitted wave to the incident wave is 
A)   2 
B)   1 
C)   0.5 
D)     
E)    " class="answers-bank-image d-inline" rel="preload" >

Question 9

A particle of mass m is confined in a two-dimensional box that has sides Lx = L and Ly = 2L. By what factor is the energy of the 3rd excited state larger than the energy of the ground state?

Accepted Answer

A)   5/4
B)   13/5
C)   17/4
D)   17/5
E)   4

Question 10

The ground-state wave function of the harmonic oscillator is

Accepted Answer

A)   0(x)  = A0e-ax  
C)    \Psi 0(x)  = A0sin(ax)  
D)    \Psi 0(x)  = A0sin(ax2)  
E)     " class="answers-bank-image d-inline" rel="preload" >
B)    Ψ\PsiΨ 0(x)  = A0e-ax 
C)    Ψ\PsiΨ 0(x)  = A0sin(ax) 
D)    Ψ\PsiΨ 0(x)  = A0sin(ax2) 
E)   0(x)  = A0e-ax  
C)    \Psi 0(x)  = A0sin(ax)  
D)    \Psi 0(x)  = A0sin(ax2)  
E)     " class="answers-bank-image d-inline" rel="preload" >

Question 11

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 excited state.

Accepted Answer

A)   1.7 eV
B)   2.2 eV
C)   6.2 eV
D)   3.0 eV
E)   None of these is correct.

Question 12

An electron of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0) and width a. If the potential barrier is reduced to 2E0, by what factor will the probability of penetration of the barrier be changed?

Accepted Answer

A)   0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0)  and width a. If the potential barrier is reduced to 2E0, by what factor will the probability of penetration of the barrier be changed? 
A)     
B)     
C)     
D)     
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" >
B)   0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0)  and width a. If the potential barrier is reduced to 2E0, by what factor will the probability of penetration of the barrier be changed? 
A)     
B)     
C)     
D)     
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" >
C)   0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0)  and width a. If the potential barrier is reduced to 2E0, by what factor will the probability of penetration of the barrier be changed? 
A)     
B)     
C)     
D)     
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" >
D)   0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0)  and width a. If the potential barrier is reduced to 2E0, by what factor will the probability of penetration of the barrier be changed? 
A)     
B)     
C)     
D)     
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" >
E)   None of these is correct.

Question 13

In order to solve the Schrödinger's equation, which of the following quantity(ies) must be specified?

Accepted Answer

A)   the kinetic energy function of the particle
B)   the potential energy function of the particle
C)   the boundary conditions
D)   (
A)   and (
B)  
E)   (
B)   and (
C)

Question 14

You put 5 non-interacting identical fermions each of mass m into a 1-d box of dimension L. You then put 10 non-interacting bosons each of mass m into a 1-d box of length 2L. Which system has the lowest ground-state energy and what is the value of the fermion system ground-state energy divided by the boson system ground-state energy?

Accepted Answer

A)   fermion system, 19/10
B)   boson system, 10/19
C)   boson system, 38/5
D)   fermion system, 5/19
E)   none of the above

Question 15

The penetration of the wave function beyond the edges of the finite square-well potential shown in the figure

Accepted Answer

A)   indicates that there is some small probability of finding the particle outside the well.
B)   forces us to conclude that E - U0 is negative in these regions.
C)   suggests that these regions are classically forbidden.
D)   is unexplainable classically.
E)   is described by all of the above.

Question 16

The quantum phenomenon known as the "tunnel effect" refers to

Accepted Answer

A)   highly eccentric electron orbits penetrating inner closed shells.
B)   the fine structure exhibited by many spectral lines.
C)   the small but finite probability that an  α\alphaα -particle originally within the nucleus will be found outside the nucleus.
D)   the penetration of shielding by high-energy fission neutrons.
E)   an orbital electron penetrating the nucleus and undergoing electron capture.

Question 17

The ground-state wave function of the harmonic oscillator is best represented by

Accepted Answer

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

Question 18

The wave function shown in the figure represents the n = _______ energy state of the harmonic oscillator.

Accepted Answer

A)   0
B)   1
C)   2
D)   3
E)   4

Question 19

A particle is confined in a three-dimensional box with L1 = L, L2 = 2L and L3 = 3L. The energy levels of the particle are given by

Accepted Answer

A)   1 = L, L2 = 2L and L3 = 3L. The energy levels of the particle are given by 
A)     . 
B)     . 
C)     . 
D)     . 
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" > .
B)   1 = L, L2 = 2L and L3 = 3L. The energy levels of the particle are given by 
A)     . 
B)     . 
C)     . 
D)     . 
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" > .
C)   1 = L, L2 = 2L and L3 = 3L. The energy levels of the particle are given by 
A)     . 
B)     . 
C)     . 
D)     . 
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" > .
D)   1 = L, L2 = 2L and L3 = 3L. The energy levels of the particle are given by 
A)     . 
B)     . 
C)     . 
D)     . 
E)   None of these is correct." class="answers-bank-image d-inline" rel="preload" > .
E)   None of these is correct.

Question 20

The Schrödinger equation

Accepted Answer

A)   is a partial differential equation in space and time.
B)   (like Newton's laws of motion)  cannot be derived.
C)   depends upon experimentation for its verification.
D)   relates the second space-derivative of the wave function to the first time-derivative of the wave function.
E)   All of these are correct.

Exam 15: Applications of the Schrodinger Equation

The wave function shown in the figure represents the n = _______ energy state of the harmonic oscillator.

An electron confined to a one-dimensional box of length L = 0.2 nm makes a transition from state n = 4 to state n = 3. The wavelength of the photon emitted is

The wave function for the energy level in a cubical box of side L that corresponds to the quantum numbers 1, 2, and 3 is

A particle is confined in a three-dimensional box with L₁= L₂ = 3L₃. The quantum numbers for the second excited state are

Particles that have antisymmetric wave functions and are described by the Pauli exclusion principle are called

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

The wave function shown in the figure represents the n = _______ energy state of the harmonic oscillator.

An electron of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.5E₀. The ratio of the wavelength of the transmitted wave to the incident wave is

A particle of mass m is confined in a two-dimensional box that has sides L_x = L and L_y = 2L. By what factor is the energy of the 3rd excited state larger than the energy of the ground state?

The ground-state wave function of the harmonic oscillator is

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 excited state.

In order to solve the Schrödinger's equation, which of the following quantity(ies) must be specified?

The penetration of the wave function beyond the edges of the finite square-well potential shown in the figure

The quantum phenomenon known as the "tunnel effect" refers to

The ground-state wave function of the harmonic oscillator is best represented by

The wave function shown in the figure represents the n = _______ energy state of the harmonic oscillator.

A particle is confined in a three-dimensional box with L₁= L, L₂ = 2L and L₃ = 3L. The energy levels of the particle are given by

The Schrödinger equation