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The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point , it is one of the most important model systems in quantum mechanics.
A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
The quantum harmonic oscillator; The quantum harmonic oscillator with an applied uniform field [1] The Inverse square root potential [2] The periodic potential The particle in a lattice; The particle in a lattice of finite length [3] The Pöschl–Teller potential; The quantum pendulum; The three-dimensional potentials The rotating system The ...
For example, a quantum harmonic oscillator may be in a state |ψ for which the expectation value of the momentum, | ^ | , oscillates sinusoidally in time. One can then ask whether this sinusoidal oscillation should be reflected in the state vector | ψ , the momentum operator p ^ {\displaystyle {\hat {p}}} , or both.
The book has also been suggested as a complement to simplified introductory books in quantum mechanics. [ 3 ] Experimental physicist and 2022 Nobel laureate in Physics Alain Aspect , has frequently mentioned that the book was a revelation early in his career, helping him better understand the research papers of quantum mechanics and the work of ...
The category of quantum models encompasses a variety of exactly solvable problems in quantum mechanics. Each exactly solvable problem is of interest for several reasons. It provides a test case for methods applicable to other problems. It can be used as a starting point for perturbation theory.
The solid plot represents the quantum mechanical probability density, while the dotted line represents the classical probability density. The dashed vertical lines indicate the classical turning points of the system. Starting with the example used in the derivation above, the simple harmonic oscillator has the potential energy function
Download as PDF; Printable version; ... Principles of Quantum Mechanics is a textbook by Ramamurti Shankar. [1] ... The Harmonic Oscillator;