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I had solve only half part of (I). That I have uploaded.
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qm 2019.3
3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom ot...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such ...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such that the spin eigenstates are split in energy by hwo (let's label the ground state |0) and the excited state |1)). The Hamiltonian for the system is written as hwo Zeeman - _ here and below. ơng,z are the usual Pauli matrices. A second, oscillating field is applied in the transverse plane, giving rise to a time-dependent term in the Hamiltoniain hw Rabi-...
(10 points) A spin-1/2 particle is originally in the ground state of the Hamiltonian Ho woS...
(10 points) A spin-1/2 particle is originally in the ground state of the Hamiltonian Ho woS At time t - 0 the system is perturbed by Here and above s, are the spin matrices. Consider H, as a small perturbation of Ho i.e., ao > wi, Find the probability for the particle to flip its spin under the perturbation at t n oo.
QM HAmiltonian, perturbation 2A where the first term is the dot product of two vectors of...
QM HAmiltonian, perturbation
2A where the first term is the dot product of two vectors of operators S1 and 52, W where the first term is the dot product of two vectors of operators Š and S2, which would book. The relative sign in the second term is due to the opposite electric charges of the par a) ) Find the energy eigenvalues and eigenstates of this system. V There are two states with the same energy. Suppose you perturbed...
Problem 2. (20 points) Consider a spin-1/2 particle with gyromagnetic ratio γ in a magnetic field B- Bi+B,k . (a) Treat...
Problem 2. (20 points) Consider a spin-1/2 particle with gyromagnetic ratio γ in a magnetic field B- Bi+B,k . (a) Treating Bi as a perturbation, (i) (6 points) calculate the first-order and second-order shift in energy and (ii) (4 points) calculate the first-order energy shift in wave function for the ground state. (b) (10 points) Solve the energy eigenvalue problem exactly, and compare the exact answers expended to the corresponding orders.
Problem 2. (20 points) Consider a spin-1/2 particle with...
pls solve asap .. thanks A spin-particle is fixed in space with the Hamiltonian H =...
pls solve asap .. thanks
A spin-particle is fixed in space with the Hamiltonian H = as, + b($+$3), where a and b are constants and as usual, Sx, Sy, S, are the operators which gives the x-, y-, z-components of the total spin. a) Write the matrix representation of Hamiltonian, H. [6 marks] b) Determine the energy levels of this system. [2 marks] c) List all possible energy levels of this system [2 marks] (Show proper construction of the...
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...
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...
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be ...
Problem 7.49
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where | z) are the eigenstates of the operator of the spin z-component $z. 1. Show that [V) is properly normalized, i.e. (W14) = 1. 2. Calculate the probability that a measurement of $x = 6x yields 3. Calculate the expectation value (Šx) for the state 14) and its dispersion ASx = V(@z) – ($()2. 4. Assume that the spin is placed in the magnetic...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such that the spin eigenstates are split in energy by hwo (let's label the ground state |0) and the excited state |1)). The Hamiltonian for the system is written as hwo Zeeman - _ here and below. ơng,z are the usual Pauli matrices. A second, oscillating field is applied in the transverse plane, giving rise to a time-dependent term in the Hamiltoniain hw Rabi-...
(10 points) A spin-1/2 particle is originally in the ground state of the Hamiltonian Ho woS At time t - 0 the system is perturbed by Here and above s, are the spin matrices. Consider H, as a small perturbation of Ho i.e., ao > wi, Find the probability for the particle to flip its spin under the perturbation at t n oo.
QM HAmiltonian, perturbation
2A where the first term is the dot product of two vectors of operators S1 and 52, W where the first term is the dot product of two vectors of operators Š and S2, which would book. The relative sign in the second term is due to the opposite electric charges of the par a) ) Find the energy eigenvalues and eigenstates of this system. V There are two states with the same energy. Suppose you perturbed...
Problem 2. (20 points) Consider a spin-1/2 particle with gyromagnetic ratio γ in a magnetic field B- Bi+B,k . (a) Treating Bi as a perturbation, (i) (6 points) calculate the first-order and second-order shift in energy and (ii) (4 points) calculate the first-order energy shift in wave function for the ground state. (b) (10 points) Solve the energy eigenvalue problem exactly, and compare the exact answers expended to the corresponding orders.
Problem 2. (20 points) Consider a spin-1/2 particle with...
pls solve asap .. thanks
A spin-particle is fixed in space with the Hamiltonian H = as, + b($+$3), where a and b are constants and as usual, Sx, Sy, S, are the operators which gives the x-, y-, z-components of the total spin. a) Write the matrix representation of Hamiltonian, H. [6 marks] b) Determine the energy levels of this system. [2 marks] c) List all possible energy levels of this system [2 marks] (Show proper construction 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...
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...
Problem 7.49
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where | z) are the eigenstates of the operator of the spin z-component $z. 1. Show that [V) is properly normalized, i.e. (W14) = 1. 2. Calculate the probability that a measurement of $x = 6x yields 3. Calculate the expectation value (Šx) for the state 14) and its dispersion ASx = V(@z) – ($()2. 4. Assume that the spin is placed in the magnetic...
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