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Quantum Harmonic OscillatorAll functions are free

Quantum Harmonic Oscillator

Calculates equally spaced energy levels, zero point energy and average occupancy number of thermal excitations.

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Ideal one-dimensional resonator, Bose thermal balance; does not contain anharmonicity.

Quantum Harmonic Oscillator: uses and methods

Calculates equally spaced energy levels, zero point energy and average occupancy number of thermal excitations.

Applicable scope and calculation boundary

Ideal one-dimensional resonator, Bose thermal balance; does not contain anharmonicity.

model and reference method

En=ℏω(n+1/2); nbar=1/[exp(ℏω/kT)−1]

model version: 1.1.0. The results are used for scientific research, exploration and teaching, please interpret according to the model conditions.

input parameters

frequency(THz)
Value range: 0.000001 – 1000000
temperature(K)
Value range: 0.0001 – 1000000

How to use

  1. Load the example or enter data that matches the field description.
  2. Confirm units and models, run calculations and check diagnostics.
  3. Export charts, tables or results packages and record model versions.

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commercial application case

Industry Application · Independent Reproduction Example

Quantum Harmonic Oscillator

quantum device team compares vibrational quantum and thermal energy scales.

Public industry reference: University of Waterloo · Institute for Quantum Computing

The institution’s public research directions include: Quantum computing, algorithms, experiments and quantum information. This link serves as a portal for field background and extended learning.

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on this site

  1. Load the default example of Quantum Harmonic Oscillator and check frequency、temperature and its units.
  2. is calculated using En=ℏω(n+1/2); nbar=1/[exp(ℏω/kT)−1], and the results are compared after adjusting a single parameter.
  3. checks applicable conditions and diagnostics, and exports numerical tables, charts, and model versions for review.

Deliverables

Calculates equally spaced energy levels, zero point energy and average occupancy number of thermal excitations. delivers parameter records, calculation charts, and reproducible JSON result packages.

needs to be checked before landing

Ideal one-dimensional resonator, Bose thermal balance; does not contain anharmonicity.。

case is compiled for public industry purposes, and the reproduction steps are independent examples of this site; it does not mean that the above-mentioned institutions use or endorse this site, nor does it cite customer benefits that have not been publicly verified. The

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recommended by universities and research institutions

Quantum Science

The following is the recommended reading order of this website organized by direction relevance, public research resources and learning portals. The number is the serial number recommended by the editor, not QS, THE or paper measurement ranking; it does not represent the overall strength of the institution.

  1. 01

    University of Waterloo · Institute for Quantum Computing

    Canada

    Quantum computing, algorithms, experiments and quantum information。

    official website link accessibility check: 2026-10-03
  2. 02

    QuTech · TU Delft / TNO

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    Qubits, Quantum Computing and Network Experiments。

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  3. 03

    IBM Quantum

    International Separation on the

    Quantum hardware, software stack and open learning resources。

    official website link accessibility check: 2026-10-03

catalog compiled on 2026-10-03. Link accessibility does not equate to verification of the latest papers, admissions, or program status; please check the institution's official website for specific research teams and opportunities.

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