File:StationaryStatesAnimation.gif
Summary
Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top two rows are the lowest two energy eigenstates, and the bottom is the superposition state <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af34edf6eb80ecf19d933700680dc920de1ba115" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:20.475ex; height:3.176ex;" alt="{\displaystyle \psi _{N}=(\psi _{0}+\psi _{1})/{\sqrt {2}}}">, which is not an energy eigenstate. The right column illustrates why energy eigenstates are also called "stationary states".
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:37, 4 January 2017 | | 300 × 280 (223 KB) | 127.0.0.1 (talk) | Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top two rows are the lowest two energy eigenstates, and the bottom is the superposition state <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>ψ<!-- ψ --></mi><mrow class="MJX-TeXAtom-ORD"><mi>N</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msub><mi>ψ<!-- ψ --></mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msub><mo>+</mo><msub><mi>ψ<!-- ψ --></mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \psi _{N}=(\psi _{0}+\psi _{1})/{\sqrt {2}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af34edf6eb80ecf19d933700680dc920de1ba115" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:20.475ex; height:3.176ex;" alt="{\displaystyle \psi _{N}=(\psi _{0}+\psi _{1})/{\sqrt {2}}}"></span>, which is not an energy eigenstate. The right column illustrates why energy eigenstates are also called "stationary states". |
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