Harmonic Oscillations / Complex Numbers
... Equation (11) is known as the equation of motion for an harmonic oscillator. Generally, the equation of motion for an object is the specific application of Newton's second law to that object. Also quite generally, the classical equation of motion is a differential equation such as Eq. (11). As we sh ...
... Equation (11) is known as the equation of motion for an harmonic oscillator. Generally, the equation of motion for an object is the specific application of Newton's second law to that object. Also quite generally, the classical equation of motion is a differential equation such as Eq. (11). As we sh ...
Dispersion relation of the nonlinear Klein
... turns out to depend on the amplitude of oscillation. As a matter of fact we are considering conservative systems, for which the dynamics can be mapped to the nonlinear oscillation of a point mass in a one-dimensional potential. The main goal of this article is to explore the effects of the nonlinear ...
... turns out to depend on the amplitude of oscillation. As a matter of fact we are considering conservative systems, for which the dynamics can be mapped to the nonlinear oscillation of a point mass in a one-dimensional potential. The main goal of this article is to explore the effects of the nonlinear ...
Conf. Ser. 724 (2016) 012029 1 - The Racah Institute of Physics
... 1 ) are listed in Table 1. These quantities are also calculated for yrast states with L > 0 and exhibit similar values in each nucleus. It is evident that a large set of rotational rare earth nuclei are located in the valley of small σ fluctuations. They can be identified as candidate nuclei with an ...
... 1 ) are listed in Table 1. These quantities are also calculated for yrast states with L > 0 and exhibit similar values in each nucleus. It is evident that a large set of rotational rare earth nuclei are located in the valley of small σ fluctuations. They can be identified as candidate nuclei with an ...
![arXiv:1312.4758v2 [quant-ph] 10 Apr 2014](http://s1.studyres.com/store/data/021352507_1-d587dd4045ccae4ae6a47bb17173f358-300x300.png)
arXiv:1312.4758v2 [quant-ph] 10 Apr 2014
... problems in quantum physics. (A number of other QM A-complete problems are given in [6].) But some natural physical problems seem to have a complexity that is slightly above QM A. For example, one such problem is estimating the spectral gap of a Hamiltonian H. The spectral gap of H is the difference ...
... problems in quantum physics. (A number of other QM A-complete problems are given in [6].) But some natural physical problems seem to have a complexity that is slightly above QM A. For example, one such problem is estimating the spectral gap of a Hamiltonian H. The spectral gap of H is the difference ...
Overview of Hamiltonian Systems
... system using only the sun and two planets. This has become famously known as the “three body problem”. In the mid-20th Century three Russian mathematicians found the solution, known today as the KAM theorem. The theorem is based on invariant tori and answers the question, what happens to the invari ...
... system using only the sun and two planets. This has become famously known as the “three body problem”. In the mid-20th Century three Russian mathematicians found the solution, known today as the KAM theorem. The theorem is based on invariant tori and answers the question, what happens to the invari ...
On inelastic hydrogen atom collisions in stellar atmospheres
... the deflection of the incident electron results in an energy transfer between electrons corresponding precisely to the ionization potential. All collisions inside this impact parameter will have a larger energy transfer and thus lead to ionization and so the cross section can be easily calculated. E ...
... the deflection of the incident electron results in an energy transfer between electrons corresponding precisely to the ionization potential. All collisions inside this impact parameter will have a larger energy transfer and thus lead to ionization and so the cross section can be easily calculated. E ...
Lecture 9 - Scattering and tunneling for a delta
... particle can cross the potential barrier. This is the effect known as tunnelling. It can also be seen that if the particle energy is greater than there is still a chance that the particle will be reflected from the potential barrier. Neither of these phenomena exist in classical mechanics. The wav ...
... particle can cross the potential barrier. This is the effect known as tunnelling. It can also be seen that if the particle energy is greater than there is still a chance that the particle will be reflected from the potential barrier. Neither of these phenomena exist in classical mechanics. The wav ...
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... identify N̂ with Jz , â with J+ and â with J− . In the oscillator case we learned from these that, acting on states, ↠raises the N̂ eigenvalue by one unit while â decreases it by one unit. As we will see, Jˆ+ adds ~ to the Jˆz eigenvalue and Jˆ− subtracts ~ to the Jˆz eigenvalue. Since J2 and ...
... identify N̂ with Jz , â with J+ and â with J− . In the oscillator case we learned from these that, acting on states, ↠raises the N̂ eigenvalue by one unit while â decreases it by one unit. As we will see, Jˆ+ adds ~ to the Jˆz eigenvalue and Jˆ− subtracts ~ to the Jˆz eigenvalue. Since J2 and ...
Revision of Boltzmann statistics for a finite number of particles
... highest populated state 共here ⌬ = 2.3⫻ 10−21 J兲, and the reduced constantvolume heat capacity CV / 共3Nk兲, calculated with the exact DigammaBoltzmann distribution for the Einstein Ag-solid as a function of the temperature T 共left column兲 and the total number of particles N 共right column兲. 共a兲 The so ...
... highest populated state 共here ⌬ = 2.3⫻ 10−21 J兲, and the reduced constantvolume heat capacity CV / 共3Nk兲, calculated with the exact DigammaBoltzmann distribution for the Einstein Ag-solid as a function of the temperature T 共left column兲 and the total number of particles N 共right column兲. 共a兲 The so ...
The Hierarchy of Hamiltonians for a Restricted Class of Natanzon
... resulting functions f , f and f perfectly agree with equations (29) , (36) and (38) respectively. Notice that the particular case when = 1 trivially reduces the nth term superpotential, equation (39) to Wn = yn , with n = v n, since all the f 's become 1 once all the ain 's are checked to reduce ...
... resulting functions f , f and f perfectly agree with equations (29) , (36) and (38) respectively. Notice that the particular case when = 1 trivially reduces the nth term superpotential, equation (39) to Wn = yn , with n = v n, since all the f 's become 1 once all the ain 's are checked to reduce ...
Hamiltonians Defined as Quadratic Forms
... Remarks. 1. There exist VeR with D(V)nD(H0) = {0}. Thus, while the Hamiltonian operator we have defined is an extension of the operator sum, it may be defined on a much larger domain! 2. D(H) can be described explicitly. Let φ e Q(H^}. It is not hard to prove — Δφ and Vφ both make sense as distribut ...
... Remarks. 1. There exist VeR with D(V)nD(H0) = {0}. Thus, while the Hamiltonian operator we have defined is an extension of the operator sum, it may be defined on a much larger domain! 2. D(H) can be described explicitly. Let φ e Q(H^}. It is not hard to prove — Δφ and Vφ both make sense as distribut ...
Quantum phase transition in one-dimensional Bose
... occur since long-wavelength fluctuations of the phase destroy the off-diagonal long-range order 关4兴. In the presence of spatial confinement, however, BECs are possible in 1D, since the confinement introduces a cutoff for the longwavelength fluctuations and hence helps maintain the longrange correlat ...
... occur since long-wavelength fluctuations of the phase destroy the off-diagonal long-range order 关4兴. In the presence of spatial confinement, however, BECs are possible in 1D, since the confinement introduces a cutoff for the longwavelength fluctuations and hence helps maintain the longrange correlat ...