The quantum harmonic oscillator
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
... the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the ...
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Fractional Fourier Transform to the Time-Independent Schrodinger Equation for the Quantum Harmonic Oscillator
... In our previous work we have proved convolution theorem, inversion formula [7, 8]. In this paper we have established some new operators of fractional Fourier transform. Lastly we have solve the time- independent ...
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Robustness of system-filter separation for the feedback control of a quantum harmonic oscillator undergoing continuous position measurement
... of quantum fields [ 1 ] and precision inertial measurements [ 2 ] due to their isolation from the environment and ability to be controlled precisely using optical and magnetic ...of quantum systems, ...
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Robustness of system-filter separation for the feedback control of a quantum harmonic oscillator undergoing continuous position measurement
... of quantum fields [1] and precision inertial mea- surements [2], due to their isolation from the environ- ment and ability to be controlled precisely using optical and magnetic ...of quantum systems has ...
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The Quantum Harmonic Oscillator Stephen Webb
... The harmonic oscillator also gives the exact solution for a particle in a uniform magnetic field of a given vector potential, as that vector potential merely takes the form of a two-dimensional ...
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FLAP P11.2 The quantum harmonic oscillator
... simple harmonic oscillator is important in classical mechanics and in quantum ...simple harmonic motion (SHM) if it is displaced by a small ...
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3.7 Lindblad dynamics for the quantum harmonic oscillator
... We already briefly touched upon the idea of a Lindblad master equation in Sec. 2.2, particularly in Eq. (2.22). The Lindblad master equation is a modi- fication of von Neumann’s equation to model open quantum ...
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Ground State Energy Density of the Quantum Harmonic Oscillator
... Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque sit amet pede ac sem eleifend con- sectetuer.. Nullam elementum, urna vel im- perdiet[r] ...
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Operational Treatment of Three Dimensions Quantum Harmonic Oscillator
... 1 Introduction Oscillators is one the fundamental problems in both classical mechanics and quantum mechanics, harmonic oscillators in the former and anharmonic oscil- lators in latter [3, 2, 1]. There are ...
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Isothermal quantum dynamics: Investigations for the harmonic oscillator
... the quantum harmonic ...single quantum particle and in the more in- volved cases of indistinguishable ...the quantum Nos´e-Hoover and related techniques, we have shown that the results thus ...
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Lindblad Equation for Harmonic Oscillator: Uncertainty Relation Depending on Temperature
... Abstract Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying ...
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Quantum dynamics of the damped harmonic oscillator
... The starting point of the results presented here is a harmonic oscillator coupled to a reservoir, where the latter is a continuum of oscillators of all positive frequencies. The use of a continuum reservoir ...
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Harmonic oscillator Notes on Quantum Mechanics
... four harmonic energy levels and right side classical turning points for 1 H 35 Cl (nè = 2990 cm -1 ), 1 H 81 Br (nè = 2650 cm -1 ) and 1 H 127 I (nè = 2310 cm -1 ...decreasing harmonic frequency going from ...
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The Collatz Conjecture and the Quantum Mechanical Harmonic Oscillator
... is because the a † terms are always present whenever the operators L 3n+1 = I + L + + P appear in the composition L ∗ L ∗ . . . L ∗ . 2.4 Cycle Identities The Collatz conjecture would be false if there are nontrivial ...
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Quantum phase transitions in nonhermitian harmonic oscillator
... nonhermitian quantum systems living in infinite-dimensional Hilbert spaces in which, after an appropriate formulation of the theory, even an innovative, quantum-phase- transition-opening “wild” behavior can ...
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The Harmonic Oscillator
... }ω. (76) Since the energy depends on the sum of n x , n y , n z , any set of quantum numbers having the same sum will represent states of equal energy. The ground state, whose energy is E 000 = 3}ω/2, is not ...
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Eigenenergy values and Eigenfunctions of a one-dimensional quantum mechanical harmonic oscillator
... Abstract: Quantum mechanics is one of the branches of ...dimensional quantum mechanical harmonic oscillator without making any ...of quantum mechanics, namely the one-dimensional ...
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6. Harmonic oscillator
... principal quantum number n = 10. The classical and quantum oscillators behave differently, but in the case of large n we see that the average of quantum probability distribution is practically equal ...
Displacement and Squeeze Operators of a Three-Dimensional Harmonic Oscillator and Their Associated Quantum States
... one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed ...
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Numerical modelling of simple harmonic oscillator
... SIMPLE HARMONIC OSCILLATOR Michael (2009) explained that a simple harmonic oscillator (SHO) is a mass connected to some elastic object of negligible mass that is fixed at the other end and ...
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