Physics 880K20: Problem Set 4 Due Wednesday, February 22 by 5PM
... Due Wednesday, February 22 by 5PM 1. This problem applies to any system with harmonic oscillator modes, including real harmonic oscillators and photons, among others. Consider the Hamiltonian h̄ωa† a, where a† and a are the photon creation and annihilation operators. a† and a satisfy the commutation ...
... Due Wednesday, February 22 by 5PM 1. This problem applies to any system with harmonic oscillator modes, including real harmonic oscillators and photons, among others. Consider the Hamiltonian h̄ωa† a, where a† and a are the photon creation and annihilation operators. a† and a satisfy the commutation ...
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... Uncertainty principle – cannot know whether up or down will result Note complete loss of information of first z split information after passing through (orthogonal) y-split! ...
... Uncertainty principle – cannot know whether up or down will result Note complete loss of information of first z split information after passing through (orthogonal) y-split! ...
communication
... What can be measured in quantum mechanics? “Traditional” approach to quantum measurements: A quantum measurement is described by an observable, M, that is, a Hermitian operator acting on the state space of the system. Measuring a system prepared in an eigenstate of M gives the corresponding eigenva ...
... What can be measured in quantum mechanics? “Traditional” approach to quantum measurements: A quantum measurement is described by an observable, M, that is, a Hermitian operator acting on the state space of the system. Measuring a system prepared in an eigenstate of M gives the corresponding eigenva ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 18. Write the Schroedinger equation to be solved for H atom and solve it for its energy using a simple solution, which assumes the wave function to depend only on the distance r and not on the angles θ and φ. 19. (a) The point group of staggered confirmation of ethane is D3d. What do these letters D ...
... 18. Write the Schroedinger equation to be solved for H atom and solve it for its energy using a simple solution, which assumes the wave function to depend only on the distance r and not on the angles θ and φ. 19. (a) The point group of staggered confirmation of ethane is D3d. What do these letters D ...
Hilbert-space partitioning of the molecular one
... orbital (MO) theory, there is a sustained interest in extracting chemical atoms and functional groups from MO-based calculations. Among the most popular methods are Mullikens population analysis [1], Baders QCT [2], Hirshfeld methods [3-4], the ISA treatment [5] and Mayer’s fuzzy atoms [6]. Most met ...
... orbital (MO) theory, there is a sustained interest in extracting chemical atoms and functional groups from MO-based calculations. Among the most popular methods are Mullikens population analysis [1], Baders QCT [2], Hirshfeld methods [3-4], the ISA treatment [5] and Mayer’s fuzzy atoms [6]. Most met ...
vuletic
... with time varying (RF) electric fields. These traps are limited in size and by micromotion, residual motion inherent in these RF traps. We are developing a new technique that uses an optical standing wave to stabilize and cool a linear array of ions. Our method also allows much finer spatial resolut ...
... with time varying (RF) electric fields. These traps are limited in size and by micromotion, residual motion inherent in these RF traps. We are developing a new technique that uses an optical standing wave to stabilize and cool a linear array of ions. Our method also allows much finer spatial resolut ...
Quantum Mechanics
... Note how Planck’s constant (ħ) shows up here. Planck’s constant provides the fundamental measure of when a system is small enough to be “quantum”. Its value is ~1·10-34 J·s. ...
... Note how Planck’s constant (ħ) shows up here. Planck’s constant provides the fundamental measure of when a system is small enough to be “quantum”. Its value is ~1·10-34 J·s. ...
Problem set 2
... is real, so that we are justified in calling it a phase angle. Here ψn (t) are orthonormal eigenstates of the hamiltonians H(t) for each t with eigenvalues En (t). 2. With the same notation as above, show that Ėn = hψn |Ḣ|ψn i. ...
... is real, so that we are justified in calling it a phase angle. Here ψn (t) are orthonormal eigenstates of the hamiltonians H(t) for each t with eigenvalues En (t). 2. With the same notation as above, show that Ėn = hψn |Ḣ|ψn i. ...
Entanglement measure for rank-2 mixed states
... the LHS and RHS of Eq. 共26兲 usually differ only by about 10−4, so that the inequality is typically very close to an equality; it is not, however, an equality. Our formula for the I tangle may be immediately applied to study the entanglement for a wide class of complex quantum systems. For example, c ...
... the LHS and RHS of Eq. 共26兲 usually differ only by about 10−4, so that the inequality is typically very close to an equality; it is not, however, an equality. Our formula for the I tangle may be immediately applied to study the entanglement for a wide class of complex quantum systems. For example, c ...
HOMEWORK ASSIGNMENT 5: Solutions
... (e) Assuming that the spin-orbit interaction lifts the degeneracy of the states with different j, how many distinct energy levels make up the fine-structure of the (3p)2 state? The allowed j values are j = 0, 1, 2, so there would be 3 fine-structure levels. (f) Which j levels would shift if a contac ...
... (e) Assuming that the spin-orbit interaction lifts the degeneracy of the states with different j, how many distinct energy levels make up the fine-structure of the (3p)2 state? The allowed j values are j = 0, 1, 2, so there would be 3 fine-structure levels. (f) Which j levels would shift if a contac ...
Harmonic Oscillator Physics
... This is interesting, but we must keep in mind a number of caveats: 1. the classical density is time-dependent, and we have chosen to average over the “natural” timescale in the system, if no such scale presented itself, we would be out of luck making these comparisons, 2. Our classical temporal aver ...
... This is interesting, but we must keep in mind a number of caveats: 1. the classical density is time-dependent, and we have chosen to average over the “natural” timescale in the system, if no such scale presented itself, we would be out of luck making these comparisons, 2. Our classical temporal aver ...