<p>The quantum wavefunction of a particle in a 2D infinite potential well of dimensions L<sub>x</sub> and L<sub>y</sub>. The wavenumbers are:
</p>
<ul><li><i>n<sub>x</sub></i>=2</li>
<li><i>n<sub>y</sub></i>=2</li></ul><p>The wavefunction, shown as <i>z</i> on the plot, is given by:
</p>
<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi _{n_{x},n_{y}}=\psi _{0}\sin \left({\frac {n_{x}\pi x}{L}}\right)\sin \left({\frac {n_{y}\pi x}{L}}\right)}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>ψ<!-- ψ --></mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>x</mi></mrow></msub><mo>,</mo><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>y</mi></mrow></msub></mrow></msub><mo>=</mo><msub><mi>ψ<!-- ψ --></mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msub><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>x</mi></mrow></msub><mi>π<!-- π --></mi><mi>x</mi></mrow><mi>L</mi></mfrac></mrow><mo>)</mo></mrow><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>y</mi></mrow></msub><mi>π<!-- π --></mi><mi>x</mi></mrow><mi>L</mi></mfrac></mrow><mo>)</mo></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \psi _{n_{x},n_{y}}=\psi _{0}\sin \left({\frac {n_{x}\pi x}{L}}\right)\sin \left({\frac {n_{y}\pi x}{L}}\right)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4826bb1fe5b9b2d9f6d04e2630699766ea80c46f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:36.285ex; height:6.176ex;" alt="{\displaystyle \psi _{n_{x},n_{y}}=\psi _{0}\sin \left({\frac {n_{x}\pi x}{L}}\right)\sin \left({\frac {n_{y}\pi x}{L}}\right)}"></span>
<a href="//commons.wikimedia.org/wiki/User:Inductiveload" title="User:Inductiveload">Inductiveload</a>
2007-02-13
Own drawing, plotted in MuPad.