Quantum mechanics.
Consider a quadratic oscillator with time dependent frequency
(1).
Find the rules of selection for transitions between
eigenstates of (2). If at t=0 the system is in the ground state of
H_0, calculate the
probabilities of transition to the different excited
states.
![) 2 mwL1+esin (Bt] x H(e)= + 2m H. HCe=0) . 2)](http://img.homeworklib.com/images/99e6c4c5-f001-4935-856f-c3970329d618.png?x-oss-process=image/resize,w_560)
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Quantum mechanics. Consider a quadratic oscillator with time dependent frequency (1). Find the rules of selection...
Module 3: Quantum Numbers and Selection Rules Worksheet Concept Map: Designation of quantum states, selection rules...
Module 3: Quantum Numbers and Selection Rules Worksheet Concept Map: Designation of quantum states, selection rules for transitions. y The Cppie me teidree s Comp Mar MandChange z . Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed Values Quantum Numbers Positive integer (1,2, 3,. Principal, n (size, energy) Angular momentum, / (shape) 0 to n 1 Magnetic, m - 0, +1 0 (orientation) -1 0+1 0 0 -1 0+1 -2-10+1+2 M hyh op e...
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an...
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Consider an electron trapped by a one-dimensional harmonic potential V(x)=-5 mo?x” (where m is the electron mass, o is a constant angular frequency). In this case, the Schrödinger equation takes the following form, **...
QUANTUM MECHANICS Problem 4 Consider a one-dimensional charged harmonic oscillator. Let the coordinate be, charge be...
QUANTUM MECHANICS
Problem 4 Consider a one-dimensional charged harmonic oscillator. Let the coordinate be, charge be q, mass be m, and the frequency of the oscillator be u. (a) 79 rat t =-oo, the oscillator is in the ground state 10). A uniform electric field E along x axis is applied betweentoo andtoo with the time dependence of E being given by E(t) ー(t/ア Neglect the induced magnetic field. Find the probability that the oscillator goes to the nth excited...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre 3. Consider two identical linear oscillators with spring...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre
3. Consider two identical linear oscillators with spring constant k. The Hamiltonian is ha d k (2 + x) H 1 + + 122, 2m d. 2 where x1 and 22 are oscillator variable. (a) by changing the variables 11 = x +, 19=xY find the energies of the three lowest states of this system? (b) If the particle are with spin 1/2, which of the above three states are triplet states...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harm...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values of energy for the simple harmonic oscillator is (a) What is the energy corresponding to the ground state (3 points)? (b) What is the energy separation between the ground state and the first excited state (3 points)? (c) The selection rule allows only those transitions for which the quantum number changes by 1. What is the energy of photon necessary to make the transition...
Quantum Mechanics. Consider a one-dimensional harmonic oscillator of frequency found in the ground state. At a perturbation is activated. Obtain an expression for the expected value of as a funct...
Quantum Mechanics. Consider a one-dimensional harmonic oscillator of frequency found in the ground state. At a perturbation is activated. Obtain an expression for the expected value of as a function of time using time-dependent perturbation theory. A step by step process is deeply appreciated. The best handwriting possible, please. Thank you very much. We were unable to transcribe this imageWe were unable to transcribe this imageV (t) = Fox cos (at) We were unable to transcribe this image V (t)...
4 A nonlinear oscillator Consider a perturbed harmonic oscillator. Using x p2 H + ke? 2...
4 A nonlinear oscillator Consider a perturbed harmonic oscillator. Using x p2 H + ke? 2 + ex4 2m 1. write this Hamiltonian in terms of â and at 2. At what frequency or frequencies could this system absorb radiation if € = 0, i.e. the oscillator is unperturbed 1 3. Qualitatively, what do the states look like for the perturbed Hamiltonian? Write the new states as a sum of the unperturbed states, without worrying too much about the amplitude...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p.
[4] Consider a harmonic oscillator...
1. A quantum system goes into a time-dependent superposition of three real eigen- functions (ener...
please show how to solve #5
1. A quantum system goes into a time-dependent superposition of three real eigen- functions (energies E, E 2, E, all equally likely). Write down the total wave- function, and calculate the probability density. Express your answer in terms of the (co)sinusoidal interference terms. 2. Write down the time-dependent wavefunction for the particle a box that is in a superposition of the n = 2 and n = 4 states. Assume there is a 30%...
Module 3: Quantum Numbers and Selection Rules Worksheet Concept Map: Designation of quantum states, selection rules for transitions. y The Cppie me teidree s Comp Mar MandChange z . Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol (Property) Allowed Values Quantum Numbers Positive integer (1,2, 3,. Principal, n (size, energy) Angular momentum, / (shape) 0 to n 1 Magnetic, m - 0, +1 0 (orientation) -1 0+1 0 0 -1 0+1 -2-10+1+2 M hyh op e...
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Consider an electron trapped by a one-dimensional harmonic potential V(x)=-5 mo?x” (where m is the electron mass, o is a constant angular frequency). In this case, the Schrödinger equation takes the following form, **...
QUANTUM MECHANICS
Problem 4 Consider a one-dimensional charged harmonic oscillator. Let the coordinate be, charge be q, mass be m, and the frequency of the oscillator be u. (a) 79 rat t =-oo, the oscillator is in the ground state 10). A uniform electric field E along x axis is applied betweentoo andtoo with the time dependence of E being given by E(t) ー(t/ア Neglect the induced magnetic field. Find the probability that the oscillator goes to the nth excited...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre
3. Consider two identical linear oscillators with spring constant k. The Hamiltonian is ha d k (2 + x) H 1 + + 122, 2m d. 2 where x1 and 22 are oscillator variable. (a) by changing the variables 11 = x +, 19=xY find the energies of the three lowest states of this system? (b) If the particle are with spin 1/2, which of the above three states are triplet states...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values of energy for the simple harmonic oscillator is (a) What is the energy corresponding to the ground state (3 points)? (b) What is the energy separation between the ground state and the first excited state (3 points)? (c) The selection rule allows only those transitions for which the quantum number changes by 1. What is the energy of photon necessary to make the transition...
4 A nonlinear oscillator Consider a perturbed harmonic oscillator. Using x p2 H + ke? 2 + ex4 2m 1. write this Hamiltonian in terms of â and at 2. At what frequency or frequencies could this system absorb radiation if € = 0, i.e. the oscillator is unperturbed 1 3. Qualitatively, what do the states look like for the perturbed Hamiltonian? Write the new states as a sum of the unperturbed states, without worrying too much about the amplitude...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p.
[4] Consider a harmonic oscillator...
please show how to solve #5
1. A quantum system goes into a time-dependent superposition of three real eigen- functions (energies E, E 2, E, all equally likely). Write down the total wave- function, and calculate the probability density. Express your answer in terms of the (co)sinusoidal interference terms. 2. Write down the time-dependent wavefunction for the particle a box that is in a superposition of the n = 2 and n = 4 states. Assume there is a 30%...
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