Consider the three-dimensional harmonic oscillator. Indicate the energy of the base state if twelve identical particles...
Consider the three-dimensional harmonic oscillator.
Indicate the energy of the base state if twelve identical particles (spin 1) are placed in the system that do not interact with each other.
Homework Answers
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Consider the three-dimensional harmonic
oscillator.
Indicate the energy of the base state if twelve
identical particles...
Quantum mechanics Consider a two-dimensional harmonic oscillator . If find the energy of the base state...
Quantum mechanics
Consider a two-dimensional harmonic oscillator
. If
find the energy of the base state until second order in theory of
disturbances and the energies of the first level excited to first
order in
.
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A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of th...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy ,...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
1. Consider one-dimensional harmonic oscillator H w(aaand its energy eigenstates are denoted as ln) , n...
1. Consider one-dimensional harmonic oscillator H w(aaand its energy eigenstates are denoted as ln) , n E No. The state of system is given by n-0 (a) Find Z. (b) Calculate the von Neumann entropy. (c) Evaluate mean energy.
3. Anharmonicity (6 marks] Consider the three-dimensional isotropic harmonic oscillator 2 1 242 р...
3. Anharmonicity (6 marks] Consider the three-dimensional isotropic harmonic oscillator 2 1 242 рґ which has energy eigenvalues En-hu(n+3/2), where n- 0,1,2.. (a) Calculate the first-order shift in the ground-state energy of the harmonic oscillator due to the addition of an anharmonic term C24 to the potential, where C> 0. (b) Calculate instead the first-order shifts in the energies of the n - 1 ercited states due to the addition of the anharmonic term C (c) For the lowest energy...
1. The two dimensional Harmonic Oscillator has the Hamiltonian n, n'>denotes the state In> of the...
Please solve with the
explanations of notations
1. The two dimensional Harmonic Oscillator has the Hamiltonian n, n'>denotes the state In> of the x-oscillator and In'> of the y-oscillator. This system is perturbed with the potential energy: Hi-Kix y. The perturbation removes the The perturbation removes the degeneracy of the states | 1,0> and |0,1> a) In first order perturbation theory find the two nondegenerate eigenstates of the full b) Find the corresponding energy eigenvalues. На Hamiltonian as normalized linear...
Seven identical particles are placed in a one-dimensional well with infinite potential: the spatial size of...
Seven identical particles are placed in a one-dimensional well with infinite potential: the spatial size of the well is L = 1 nm. Calculate the energy of the base state for the system, if the particles are a) electrons b) pions (which are bosons) with mass = 264 and electron mass
Please do this problem about quantum mechanic harmonic oscillator and show all your steps thank you. Q1. Consider a particle of mass m moving in a one-dimensional harmonic oscillator potential. 1....
Please do this problem about quantum mechanic harmonic
oscillator and show all your steps thank you.
Q1. Consider a particle of mass m moving in a one-dimensional harmonic oscillator potential. 1. Calculate the product of uncertainties in position and momentum for the particle in 2. Compare the result of (a) with the uncertainty product when the particle is in its the fifth excited state, ie. (OxơP)5. lowest energy state.
Q1. Consider a particle of mass m moving in a one-dimensional...
2. Consider a one-dimensional simple harmonic oscillator. Do the following algebraically. 2. Consider a one -dimensional...
2. Consider a one-dimensional simple harmonic oscillator. Do the
following algebraically.
2. Consider a one -dimensional simple harmonic oscillator. Do the following algebraically. a) Construct a linear superposition of I0) and |1) by choosing appropriate phases, such that (x) is as large as possible. i) Suppose the oscillator is in the state la) att 0. Find la) and x) ii) Evaluate the expectation value(x) at t 〉 0. ii Evaluate (A x)2) att > 0. b) Answer the same questions...
2. Two noninteracting particles, each of mass m, are in the 1-D harmonic oscillator potential Describe...
2. Two noninteracting particles, each of mass m, are in the 1-D harmonic oscillator potential Describe their ground state and the next two excited states, that is, their corresponding (i) wave functions, (i) energy eigenvalues, and (ii) degeneracies if two particles are (a) distinguishable particles, (b) the identical bosons, and (c) the identical fermions. 3. Suppose one particle is in the ground state, and the other is in the first excited state for tw particles described in Prob. 2. Calculate...
Quantum mechanics
Consider a two-dimensional harmonic oscillator
. If
find the energy of the base state until second order in theory of
disturbances and the energies of the first level excited to first
order in
.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
1. Consider one-dimensional harmonic oscillator H w(aaand its energy eigenstates are denoted as ln) , n E No. The state of system is given by n-0 (a) Find Z. (b) Calculate the von Neumann entropy. (c) Evaluate mean energy.
3. Anharmonicity (6 marks] Consider the three-dimensional isotropic harmonic oscillator 2 1 242 рґ which has energy eigenvalues En-hu(n+3/2), where n- 0,1,2.. (a) Calculate the first-order shift in the ground-state energy of the harmonic oscillator due to the addition of an anharmonic term C24 to the potential, where C> 0. (b) Calculate instead the first-order shifts in the energies of the n - 1 ercited states due to the addition of the anharmonic term C (c) For the lowest energy...
Please solve with the
explanations of notations
1. The two dimensional Harmonic Oscillator has the Hamiltonian n, n'>denotes the state In> of the x-oscillator and In'> of the y-oscillator. This system is perturbed with the potential energy: Hi-Kix y. The perturbation removes the The perturbation removes the degeneracy of the states | 1,0> and |0,1> a) In first order perturbation theory find the two nondegenerate eigenstates of the full b) Find the corresponding energy eigenvalues. На Hamiltonian as normalized linear...
Please do this problem about quantum mechanic harmonic
oscillator and show all your steps thank you.
Q1. Consider a particle of mass m moving in a one-dimensional harmonic oscillator potential. 1. Calculate the product of uncertainties in position and momentum for the particle in 2. Compare the result of (a) with the uncertainty product when the particle is in its the fifth excited state, ie. (OxơP)5. lowest energy state.
Q1. Consider a particle of mass m moving in a one-dimensional...
2. Consider a one-dimensional simple harmonic oscillator. Do the
following algebraically.
2. Consider a one -dimensional simple harmonic oscillator. Do the following algebraically. a) Construct a linear superposition of I0) and |1) by choosing appropriate phases, such that (x) is as large as possible. i) Suppose the oscillator is in the state la) att 0. Find la) and x) ii) Evaluate the expectation value(x) at t 〉 0. ii Evaluate (A x)2) att > 0. b) Answer the same questions...
2. Two noninteracting particles, each of mass m, are in the 1-D harmonic oscillator potential Describe their ground state and the next two excited states, that is, their corresponding (i) wave functions, (i) energy eigenvalues, and (ii) degeneracies if two particles are (a) distinguishable particles, (b) the identical bosons, and (c) the identical fermions. 3. Suppose one particle is in the ground state, and the other is in the first excited state for tw particles described in Prob. 2. Calculate...
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