graph d below a possible wavefunction for an electron in a 1D infinite square well between and at time It is a possible wavefunction It is not a possible wavefunction ID: 692751
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Slide1
Concept test 14.1Is the function graph d below a possible wavefunction for an electron in a 1-D infinite square well between and at time ?It is a possible wavefunction.It is not a possible wavefunction because it does not satisfy the Time-independent Schroedinger Equation.It is not possible because it is neither symmetric nor anti-symmetric about the center of the well. It is not a possible wave function because it does not satisfy the boundary conditions of the system.None of the above
Slide2
Concept Test 14.2Choose all of the following statements that are correct about the wave function shown below for an electron interacting with an infinite square well of width between andat time . and are continuous everywhere.It is a possible wave function because it is a continuous, smooth and normalizable function that satisfies the boundary conditions.It is a possible wave function, and can be obtained by a superposition of energy eigenfunctions according to Fourier series analysis.It
is not a possible wave function because it is neither symmetric nor
antisymmetric
about the center of the well.(I) only B. (II) only C. (III) only D. (I) and (II) onlyE. None of the above.
Slide3
Concept Test 14.3An electron is interacting with a one dimensional finite square well with a wave function at t = 0. Choose all of the following statements that are correct: must be symmetric about the center of the well. must reflect the symmetry of the potential energy well.Any single-valued, smooth normalizable function is a possible wavefunction .(I)
only B. (II)
only C. (III
) only D. (I) and (III) only E. (II) and (III) only Slide4
Concept Test 14.4Choose all of the following statements that are correct about the wave function shown below for an electron interacting with a finite square well of width (when and anywhere elseat time : It is a possible wave function because it is the first excited state.It is a possible wave function because it is anti-symmetric about the center of the well.It is not a possible wave function because it goes to zero at the boundaries of the well.It
is not a possible wave function because its derivative is not continuous at the boundaries of the well
.
(I) only B. (III) only C. (IV) only D. (I) and (II) only E. (III) and (IV) only Slide5
Concept Test 14.5Choose all of the following statements that are correct about the wave function shown below for an electron interacting with a finite square well of width a (when and anywhere else). and are continuous and single valued everywhere.
Smooth function that goes to zero within the region x=
0 and
x=a.It is a possible wave function because it is a continuous, smooth and normalizable function that satisfies the boundary conditions.It is not a possible wave function because it doesn’t satisfy the boundary conditions; it goes to zero inside the well.It is not a possible wave function because the probability of finding the particle outside the finite square well is zero but quantum mechanically it must be
nonzero.
A. (I
)
only B. (II
)
only C. (III
)
only D. (II
) and (III)
only E. None
of the above.
Slide6
Concept test 14.6Choose all of the following wave functions that are possible wave functions for an electron in a one dimensional infinite square well of width (boundaries between and ) at time:(I) only(I) and (II) only(I) and (III) only(II) and (III) onlyAll of the above Slide7
Concept Test 14.7Choose all of the following statements are true about a particle interacting with a double delta function potential energy barrier, as shown below:It is possible to find the particle in all three regions.If the particle starts out in region II, then the particle is in a bound state.The energy levels for this system are discrete.A. (I) only B. (II) only C. (III) only D. (II) and (III) only E. None of the aboveV(x)x
I
II
IIISlide8
Concept test 14.8Suppose at time , the initial wavefunction of an electron in a 1D infinite square well is , where and are the ground state and first excited state wavefunctions. Choose all of the following statements that are correct if you measure the energy at .You can obtain any of the allowed energies , You can obtain only or with equal probability.
You can obtain only
You can obtain only
None of the above.
Slide9
Concept test 14.9Suppose at time , the initial wavefunction of an electron in a 1D infinite square well is , where and are the ground state and first excited state wavefunctions. If you measure the energy at time t=0, which one of the following statements is correct?The wavefunction will become either or
immediately after the measurement and the system will remain in that state at future times.
The
wavefunction will become either or immediately after the measurement and the system will go back to
after a long time.
The
wavefunction
will become either
or
immediately after the measurement and the system will
evolve into a state which is
superposition of all the stationary states after a long time.
The
wavefunction
will become a delta function immediately after the energy measurement and the system will stay in that state for all future times.
The
wavefunction
will become a delta function immediately after the energy measurement and go back to
after a certain time.
Slide10
Concept test 14.10Suppose at time , the initial wavefunction of an electron in a 1D infinite square well is , where and are the ground state and first excited state wavefunctions. Choose all of the following statements that are correct about the expectation value of the energy of the system at t=0.
A. 1 only B. 2 only C. 3 only D. 1 and 3 only E. 2 and 3 only
Slide11
Concept test 14.11Suppose and are the ground state and first excited state wavefunctions of an electron in a 1D infinite square well of width a. Choose all of the following functions that represent the same state as .
A. 1 only B. 2 only C. 3 only D. 1 and 3 only E. none of the above
Slide12
Concept test 14.12Suppose is an eigenfunction of the position operator with eigenvalue . Choose all of the following statements that are correct.
1 only B. 3 only C. 4 only D
.
1 and 2 only E. 1, 2, and 4 only Slide13
Concept test 14.13Choose all of the following statements that are correct about an electron in an eigenstate of the position operator.The energy of the electron is well defined because he position operator commutes with the Hamiltonian.The momentum of the electron cannot be well defined in this state due to the uncertainty principle.The measurement of position will yield a definite value with 100% certainty.1 only B. 1 and 2 only C. 1 and 3 only D. 2 and 3 only E. All of the above.