Isotropic harmonic oscillator
[DOCX File]Welcome to Central University of Punjab, Bathinda
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Isotropic Harmonic oscillator. Degeneracy. Matrix Mechanics: Postulates of quantum mechanics. Hilbert space. Matrix representation of wave functions and operators. Dirac bra and Ket notations. Change of basis. Harmonic oscillator problem in matrix mechanics creation, destruction and number operators. Orbital angular momentum operators in their ...
[DOC File]Brief Introduction
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Solution of Harmonic oscillator using wave mechanics and matrix mechanics: matrix representation and eigen values of various operators, Anisotropic and isotropic harmonic oscillator, The box potential.
2D Quantum Harmonic Oscillator
Harmonic oscillator states in 1D are usually labeled by the quantum number “n”, with “n=0” being the ground state [since ]. But in this problem, 1s means the ground state and 2p means the component of the first excited state, named in analogy to the hydrogen atom …
Problem 1 (20 points) - Purdue University
Non-isotropic harmonic oscillator. More generally, the force constants may not be the same in the three directions.. The separated equations of motion are. These have solutions of the same form, but different constants. where , , and .
[DOC File]Nuclear Models - Università degli Studi di Pavia
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Problem 1 (30 points). The initial conditions of a two-dimensional isotropic oscillator are as follows: where ( is the angular frequency. (20 points) Find x and y as functions of t ... (10 points) Show that the particle executes simple harmonic motion and calculate the period of the motion (Ignore any effects of rotation). (a) The derivation of ...
[DOC File]Physics 201 2009
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Let be the annihilation and creation operators of a two-dimensional, isotropic, harmonic oscillator: We write. J1, J2, J3 may be considered as the Cartesian coordinates of a certain vector operator . Show that the components of verify the commutation relations characteristic of an …
[DOC File]The 3D Harmonic Oscillator - University of Chicago
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Figure 5 - Splitting of the energy levels of the three-dimensional isotropic harmonic oscillator by spin-orbit coupling. The numbers in parentheses and brackets have the same meaning as in figure 4, the "magic numbers" are given on the far right. Level Order. There are several important features of this energy level diagram.
[DOC File]PC4201 QUANTUM MECHANICS
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Interbasis expansions for isotropic harmonic oscillator, Phys. Lett. A 376, 1262(2012). 150. Wen-Chao Qiang, Guo-Hua Sun and Shi-Hai Dong, Real exact solutions to the relativistic spinless particle with modified Rosen-Morse potential . and its PT symmetry, Annalen del Physik 524, 360(2012). 151. Gao-Feng Wei, Guo-Hua Sun and Shi-Hai Dong,
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