Test Your Knowledge
1.
Answer the following questions for a particle in a box with infinite walls.
A.
Write the wave function for ground state and the 1st excited state.
B.
Draw the wave function for 1st excited state
1C.
Draw the probability distribution for a particle in the 3rd excited state.
1D.
What is the probability for finding a particle in the 3rd excited state between x= 0
and x=L/4?
1E.
Draw an energy diagram showing the first 4 energy states for an electron confined
in a well whose length is 2 nm.
1F.
For problem 1E find the wavelength of the photon emitted when the electron
moves from the 2nd excited state to the ground state.
2.
For an electron trapped in a finite well of length L and height Vo,
A.
Draw a qualitative sketch for the wave function of the 3rd excited state.
B.
Draw a qualitative sketch for the probability distribution for the 3rd excited state.
C.
What is the expectation value for position of the electron in this state?
2D.
Approximate the energy of an electron trapped in the 3rd excited state of a finite
square well with potential height 3.6 eV and width 0.25 nm.
3.
A particle with an energy of 6 eV encounters a potential barrier as shown below:
Uo = 10eV
E = 6 eV
U=0
x=0
A.
Write the Time-Independent Schrodinger Equation for
Region I:
Region II:
B.
Write the General Solution to the Schrodinger Equation for
Region I:
Region II:
3C.
Write all the necessary boundary and normalization conditions to solve for all the
coefficients in the General Solution.
D.
Graph a qualitative sketch of the wave function for this problem
4.
A particle with an energy of 10 eV encounters a potential barrier as shown below:
E = 10 eV
Uo = 6eV
U=0
x=0
A.
Write the Time-Independent Schrodinger Equation for
Region I:
Region II:
B.
Write the General Solution to the Schrodinger Equation for
Region I:
Region II:
4C.
Write all the necessary boundary and normalization conditions to solve for all the
coefficients in the General Solution.
D.
Graph a qualitative sketch of the wave function for this problem
5.
A particle with an energy of 5 eV encounters a potential barrier as shown below:
U = 8eV
E = 5 eV
U=0
x=0
A.
x=L
Write the Time-Independent Schrodinger Equation for
Region I:
Region II:
Region III:
B.
Write the General Solution to the Schrodinger Equation for
Region I:
Region II:
Region III:
U = 3eV
5C.
Write all the necessary boundary and normalization conditions to solve for all the
coefficients in the General Solution.
D.
Graph a qualitative sketch of the wave function for this problem