Question 1

A particle's wave function is   .What is its momentum at the origin?

Accepted Answer

A)    
B)    
C)    
D)    
E) It is impossible to determine with given information. 
A)    
B)    
C)    
D)    
E) It is impossible to determine with given information.

Question 2

An electron is confined in an infinite square well between x = 0 and x =   .The wave function of the electron is   .Which of the following could be the value of A if the wave function is normalized?

Accepted Answer

A)    
B) 1 
C)    
D)    
E)    
A)    
B) 1 
C)    
D)    
E)

Question 3

A proton is incident on a 10 fm wide energy barrier.If the proton's energy is 1 MeV below the top of the barrier,what is the probability that the proton will tunnel through the barrier?

Accepted Answer

A) 12.2% 
B) 8.5% 
C) 5.9% 
D) 1.2% 
A) 12.2% 
B) 8.5% 
C) 5.9% 
D) 1.2%

Question 4

What is the probability that a particle whose wave function $\Psi$(x)= A(x-2)2 for x between 0 and 1,and otherwise,$\Psi$(x)= 0,is found at x > 0.5?

Accepted Answer

A) 21.3% 
B) 26.0% 
C) 33.9% 
D) 48.6% 
E) 50.0% 
A) 21.3% 
B) 26.0% 
C) 33.9% 
D) 48.6% 
E) 50.0%

Question 5

As the wave number of a particle's probability wave function increases,what always happens?

Accepted Answer

A) The magnitude of the particle's momentum increases. 
B) The particle's kinetic energy increases. 
C) Both A and B are correct. 
D) Neither A nor B is correct. 
A) The magnitude of the particle's momentum increases. 
B) The particle's kinetic energy increases. 
C) Both A and B are correct. 
D) Neither A nor B is correct.

Question 6

Consider an electron that is confined to the x-y plane by a two-dimensional rectangular infinite potential well.The width of the well is L in the x-direction and 3 L in the y-direction.What is the lowest energy which is shared by more than one distinct state, i.e.,two or more different states have the same energy?

Accepted Answer

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

Question 7

A surface is examined using a scanning tunneling microscope (STM).For the range of the working gap,L,between the tip and the sample surface,assume that the electron wave function for the atoms under investigation falls off exponentially as   .The tunneling current through the STM tip is proportional to the tunneling probability.In this situation,the ratio of the current when the STM tip is 0.465 nm above a surface feature to the current when the tip is 0.425 nm above the surface is

Accepted Answer

A) 0.336 
B) 0.301 
C) 0.314 
D) 0.408 
E) 0.671 
A) 0.336 
B) 0.301 
C) 0.314 
D) 0.408 
E) 0.671

Exam 37: Quantum Mechanics

A particle's wave function is .What is its momentum at the origin?

An electron is confined in an infinite square well between x = 0 and x = .The wave function of the electron is .Which of the following could be the value of A if the wave function is normalized?

A proton is incident on a 10 fm wide energy barrier.If the proton's energy is 1 MeV below the top of the barrier,what is the probability that the proton will tunnel through the barrier?

What is the probability that a particle whose wave function Ψ\PsiΨ (x)= A(x-2)2 for x between 0 and 1,and otherwise, Ψ\PsiΨ (x)= 0,is found at x > 0.5?

As the wave number of a particle's probability wave function increases,what always happens?

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What is the probability that a particle whose wave function $\Psi$ (x)= A(x-2)² for x between 0 and 1,and otherwise, $\Psi$ (x)= 0,is found at x > 0.5?