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  2. Quantum harmonic oscillator - Wikipedia

    en.wikipedia.org/wiki/Quantum_harmonic_oscillator

    The Hooke's atom is a simple model of the helium atom using the quantum harmonic oscillator. Modelling phonons, as discussed above. A charge q {\displaystyle q} with mass m {\displaystyle m} in a uniform magnetic field B {\displaystyle \mathbf {B} } is an example of a one-dimensional quantum harmonic oscillator: Landau quantization .

  3. Harmonic oscillator - Wikipedia

    en.wikipedia.org/wiki/Harmonic_oscillator

    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.

  4. List of quantum-mechanical systems with analytical solutions

    en.wikipedia.org/wiki/List_of_quantum-mechanical...

    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 ...

  5. Wave function - Wikipedia

    en.wikipedia.org/wiki/Wave_function

    For the harmonic oscillator, x and p enter symmetrically, so there it does not matter which description one uses. The same equation (modulo constants) results. From this, with a little bit of afterthought, it follows that solutions to the wave equation of the harmonic oscillator are eigenfunctions of the Fourier transform in L 2. [nb 5]

  6. Coherent state - Wikipedia

    en.wikipedia.org/wiki/Coherent_state

    In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in ...

  7. Perturbation theory (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory...

    The Hamiltonians to which we know exact solutions, such as the hydrogen atom, the quantum harmonic oscillator and the particle in a box, are too idealized to adequately describe most systems. Using perturbation theory, we can use the known solutions of these simple Hamiltonians to generate solutions for a range of more complicated systems.

  8. Molecular vibration - Wikipedia

    en.wikipedia.org/wiki/Molecular_vibration

    See quantum harmonic oscillator for graphs of the first 5 wave functions, which allow certain selection rules to be formulated. For example, for a harmonic oscillator transitions are allowed only when the quantum number n changes by one, = but this does not apply to an anharmonic oscillator; the observation of overtones is only possible because ...

  9. Hamiltonian system - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_system

    One example is the planetary movement of three bodies: while there is no closed-form solution to the general problem, Poincaré showed for the first time that it exhibits deterministic chaos. Formally, a Hamiltonian system is a dynamical system characterised by the scalar function H ( q , p , t ) {\displaystyle H({\boldsymbol {q}},{\boldsymbol ...