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Determine the wave function and energy for the second excited level of a particle in a...
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0...
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0 three-dimensional cubic box (Lx=Ly=L2), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level? (B) 1 (C)2 (D) 3 (E) 4 (A) 0
Figure 8.3 gives the energy and degeneracy of the first 5 levels for a particle in...
Figure 8.3 gives the energy and degeneracy of the
first 5 levels for a particle in a cubic box. Find the energy and
degeneracy of the next 3 levels (that is the 6th, 7th and
8th).
m? Degeneracy 4E.. 12 None 3 SE 93 2E0 6 Eo. None Figure 8.3 An energy-level di- agram for a particle confined to a cubic box. The ground-state energy is Ep = 37'h/2m/?. and ?? ni + n + n. Note that most of...
II.6. The wave function of a particle in a 1D rigid box (infinite potential well) of...
II.6. The wave function of a particle in a 1D rigid box (infinite potential well) of length L is: v, 8, 1) = sin(x)e-En/5). n = 1,2,3... What is the probability density of finding the particle in its 2nd excited state?
Determine the energy of the particle if the proposed wave function satisfies the Schrödinger equation for x < 0.
A fellow student proposes that a possible wave function for a free particle with mass \(m\) (one for which the potential-energy function \(U(x)\) is zero ) is$$ \psi(x)=\left\{\begin{array}{ll} e^{-k x}, & x \geq 0 \\ e^{+\kappa x}, & x<0 \end{array}\right. $$where \(\kappa\) is a positive constant. (a) Graph this proposed wave function.(b) Determine the energy of the particle if the proposed wave function satisfies the Schrödinger equation for \(x<\)0.(c) Show that the proposed wave function also satisfies the Schrödinger equation...
QM 30 Relating classical and quantum mechanics IV. Supplement: Highly-excited energy eigenstates A particle is in...
QM 30 Relating classical and quantum mechanics IV. Supplement: Highly-excited energy eigenstates A particle is in the potential well shown at right A. First, treat this problem from a purely elassical standpoint (assume the particle has enough energy to reach both regions) Give an example of a real physical situation that corresponds to this potential well. 1. region I | region II 2. In which region of the well would the particle have greater kinetic energy? Explain. 3. In which...
The particle in a box model is often used to make rough estimates of energy level...
The particle in a box model is often used to make rough estimates of energy level spacings. For a metal wire 10.0 cm long, treat a conduction electron as a particle confined to a one-dimensional box of length 10.0 cm. Which of the following shows the wave function was a function of position for the electron in this box for the ground state? We were unable to transcribe this image
For a particle in a 3D box, with lengths L = Lx = 2 Ly =...
For a particle in a 3D box, with lengths L = Lx = 2 Ly = 14 Lz, provide a general expression for the energies in terms of L, and determine the quantum numbers associated with the lowest energy level that has a degeneracy of 3.
P.18.26 Verify that the wave function for the first excited state of the harmonic oscillator is...
P.18.26 Verify that the wave function for the first excited state of the harmonic oscillator is a solution of the Schroedinger equation for that system. Determine the energy eigenvalue.
a. A particle of mass m moves freely on a line of length a il In...
a. A particle of mass m moves freely on a line of length a il In the same diagram, draw the wave function and the squared wave function for the 2nd excited state of the particle. (4 marks) ii. What is the difference between classical and quantum mechanical behavior of the particle in such a box? (3 marks) Hi. Write the expression for the energy of the particle moving freely in a box of sides a, b and c. (2...
47 (a) A particle is confined inside a rectangular box with sides of length a, a,...
47 (a) A particle is confined inside a rectangular box with sides of length a, a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave functions have this energy b) Now assume the rectangular box has sides of length a, 2a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave functions have this energy.
nh 61. The energy for one-dimensional particle-in-a-box is E=" 1. For a particle in a 0 three-dimensional cubic box (Lx=Ly=L2), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level? (B) 1 (C)2 (D) 3 (E) 4 (A) 0
Figure 8.3 gives the energy and degeneracy of the
first 5 levels for a particle in a cubic box. Find the energy and
degeneracy of the next 3 levels (that is the 6th, 7th and
8th).
m? Degeneracy 4E.. 12 None 3 SE 93 2E0 6 Eo. None Figure 8.3 An energy-level di- agram for a particle confined to a cubic box. The ground-state energy is Ep = 37'h/2m/?. and ?? ni + n + n. Note that most of...
II.6. The wave function of a particle in a 1D rigid box (infinite potential well) of length L is: v, 8, 1) = sin(x)e-En/5). n = 1,2,3... What is the probability density of finding the particle in its 2nd excited state?
QM 30 Relating classical and quantum mechanics IV. Supplement: Highly-excited energy eigenstates A particle is in the potential well shown at right A. First, treat this problem from a purely elassical standpoint (assume the particle has enough energy to reach both regions) Give an example of a real physical situation that corresponds to this potential well. 1. region I | region II 2. In which region of the well would the particle have greater kinetic energy? Explain. 3. In which...
The particle in a box model is often used to make rough estimates of energy level spacings. For a metal wire 10.0 cm long, treat a conduction electron as a particle confined to a one-dimensional box of length 10.0 cm. Which of the following shows the wave function was a function of position for the electron in this box for the ground state? We were unable to transcribe this image
For a particle in a 3D box, with lengths L = Lx = 2 Ly = 14 Lz, provide a general expression for the energies in terms of L, and determine the quantum numbers associated with the lowest energy level that has a degeneracy of 3.
P.18.26 Verify that the wave function for the first excited state of the harmonic oscillator is a solution of the Schroedinger equation for that system. Determine the energy eigenvalue.
a. A particle of mass m moves freely on a line of length a il In the same diagram, draw the wave function and the squared wave function for the 2nd excited state of the particle. (4 marks) ii. What is the difference between classical and quantum mechanical behavior of the particle in such a box? (3 marks) Hi. Write the expression for the energy of the particle moving freely in a box of sides a, b and c. (2...
47 (a) A particle is confined inside a rectangular box with sides of length a, a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave functions have this energy b) Now assume the rectangular box has sides of length a, 2a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave functions have this energy.
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