Question 1

A particle is in the first excited state of a one-dimensional box of length 1.0 m. What is the minimum value of its momentum (in kg ⋅ m/s)?

Accepted Answer

A)  3.3 × 10−34 
B)  6.6 × 10−34 
C)  9.9 × 10−34 
D)  13 × 10−34 
E)  22 × 10−34 
A)  3.3 × 10−34 
B)  6.6 × 10−34 
C)  9.9 × 10−34 
D)  13 × 10−34 
E)  22 × 10−34

Question 2

The ground state energy of a harmonic oscillator is

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  E = 0 
E) 
  
A) 
  
B) 
  
C) 
  
D)  E = 0 
E)

Question 3

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantization of ____ of the particle.

Accepted Answer

A)  the momentum 
B)  the energy 
C)  the velocity 
D)  all of the above properties 
E)  only properties (a) and (b) 
A)  the momentum 
B)  the energy 
C)  the velocity 
D)  all of the above properties 
E)  only properties (a) and (b)

Question 4

A particle is in the second excited state of a one-dimensional box of length 1.0 m. What is its momentum (in kg ⋅ m/s)?

Accepted Answer

A)  6.6 × 10−34 
B)  3.3 × 10−34 
C)  9.9 × 10−34 
D)  13 × 10−34 
E)  cannot be solved unless mass of particle is known 
A)  6.6 × 10−34 
B)  3.3 × 10−34 
C)  9.9 × 10−34 
D)  13 × 10−34 
E)  cannot be solved unless mass of particle is known

Question 5

The graph below represents a wave function ψ(x) for a particle confined to −4.00 m ≤ x ≤ +4.00 m. The magnitude of the normalization constant A is

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E)  4. 
A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E)  4.

Question 6

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

Accepted Answer

A)  1 
B)  4 
C)  2 
D)  8 
E)  16 
A)  1 
B)  4 
C)  2 
D)  8 
E)  16

Question 7

A particle in a finite potential well has energy E, as shown below.   The wave function in region II where x > 0 has the form ψII =

Accepted Answer

A)  Ae−Cx. 
B)  AeCx. 
C)  F sin kx. 
D)  G cos kx. 
E)  F sin kx + G cos kx. 
A)  Ae−Cx. 
B)  AeCx. 
C)  F sin kx. 
D)  G cos kx. 
E)  F sin kx + G cos kx.

Question 8

The graph below represents a wave function ψ(x) for a particle confined to −2.00 m ≤ x ≤ +2.00 m. The value of the normalization constant A may be

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E)  either
  or
  . 
A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E)  either
  or
  .

Question 9

The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Ψ(x) = A sin (nπx/L) + B cos (nπx/L) . The constants A and B are determined to be

Accepted Answer

A) 
  , 0 
B) 
  ,
  
C)  0,
  
D) 
  ,
  
E)  2/L, 0 
A) 
  , 0 
B) 
  ,
  
C)  0,
  
D) 
  ,
  
E)  2/L, 0

Question 10

The wave function for a particle in a box of length L is given by   . If the box extends from x = 0 to x = L, What is the probability of finding the particle between x = 0.60 L and x = 0.70 L?

Accepted Answer

A)  0.10 
B)  0.20 
C)  0.25 
D)  0.05 
E)  The probability is not given. 
A)  0.10 
B)  0.20 
C)  0.25 
D)  0.05 
E)  The probability is not given.

Question 11

The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax. ψ(x) = 0 for x  L. When the wave function is normalized, the probability density at coordinate x has the value

Accepted Answer

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

Question 12

A particle in a finite potential well has energy E, as shown below.   The wave function in region III where x > L has the form ψIII =

Accepted Answer

A)  Ae−Cx. 
B)  AeCx. 
C)  F sin kx. 
D)  G cos kx. 
E)  F sin kx + G cos kx. 
A)  Ae−Cx. 
B)  AeCx. 
C)  F sin kx. 
D)  G cos kx. 
E)  F sin kx + G cos kx.

Question 13

Classically, the concept of "tunneling" is impossible. Why?

Accepted Answer

A)  The kinetic energy of the particle would be negative. 
B)  The velocity of the particle would be negative. 
C)  The total energy of a particle is equal to the kinetic and potential energies. 
D)  The kinetic energy must be equal to the potential energy. 
E)  The total energy for the particle would be negative. 
A)  The kinetic energy of the particle would be negative. 
B)  The velocity of the particle would be negative. 
C)  The total energy of a particle is equal to the kinetic and potential energies. 
D)  The kinetic energy must be equal to the potential energy. 
E)  The total energy for the particle would be negative.

Exam 41: Quantum Mechanics

A particle is in the first excited state of a one-dimensional box of length 1.0 m. What is the minimum value of its momentum (in kg ⋅ m/s)?

The ground state energy of a harmonic oscillator is

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantization of ____ of the particle.

A particle is in the second excited state of a one-dimensional box of length 1.0 m. What is its momentum (in kg ⋅ m/s)?

The graph below represents a wave function ψ(x) for a particle confined to −4.00 m ≤ x ≤ +4.00 m. The magnitude of the normalization constant A is

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

A particle in a finite potential well has energy E, as shown below. The wave function in region II where x > 0 has the form ψII =

The graph below represents a wave function ψ(x) for a particle confined to −2.00 m ≤ x ≤ +2.00 m. The value of the normalization constant A may be

The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Ψ(x) = A sin (nπx/L) + B cos (nπx/L) . The constants A and B are determined to be

The wave function for a particle in a box of length L is given by . If the box extends from x = 0 to x = L, What is the probability of finding the particle between x = 0.60 L and x = 0.70 L?

The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax. ψ(x) = 0 for x < 0 and x > L. When the wave function is normalized, the probability density at coordinate x has the value

A particle in a finite potential well has energy E, as shown below. The wave function in region III where x > L has the form ψIII =

Classically, the concept of "tunneling" is impossible. Why?

Physics and Measurement

Motion in One Dimension

Vectors

Motion in Two Dimensions

The Laws of Motion

Circular Motion and Other Applications of Newtons Laws

Energy of a System

Conservation of Energy

Linear Momentum and Collisions

Rotation of a Rigid Object About a Fixed Axis

Angular Momentum

Static Equilibrium and Elasticity

Universal Gravitation

Fluid Mechanics

Oscillatory Motion

Wave Motion

Superposition and Standing Waves

Temperature

The First Law of Thermodynamics

The Kinetic Theory of Gases

Heat Engines, Entropy, and the Second Law of Thermodynamics

Electric Fields

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Sources of the Magnetic Field

Faradays Law

Inductance

Alternating-Current Circuits

Electromagnetic Waves

The Nature of Light and the Principles of Ray Optics

Image Formation

Wave Optics

Diffraction Patterns and Polarization

Relativity

Introduction to Quantum Physics

Atomic Physics

Molecules and Solids

Nuclear Structure

Particle Physics and Cosmology

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A particle in a finite potential well has energy E, as shown below. The wave function in region II where x > 0 has the form ψ_II =

A particle in a finite potential well has energy E, as shown below. The wave function in region III where x > L has the form ψ_III =