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Psykat

Schrödinger Equation Physics

\[i\hbar\,\frac{\partial\Psi}{\partial t} = \hat H\,\Psi\]
$21.99 USD
$21.99 USD
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What does a quantum system do when nobody looks? Psykat evolves smoothly. The Schrödinger equation, iħ∂Ψ/∂t = ĤΨ, fixes how the wavefunction changes in time, set by the system’s energy. A measurement yields one outcome, with probabilities given by the Born rule, |Ψ|². Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

The Schrödinger equation tells you how a quantum wavefunction changes in time, driven by the system's kinetic and potential energy. The squared size of the wavefunction gives the probability of finding the particle in each place.

Psykat has two moods: evolving, and being observed.

The first line is the Schrödinger equation, which Erwin Schrödinger published in its time-dependent form in 1926. Give it the wavefunction now and the Hamiltonian, which encodes the system's energy, and it tells you the wavefunction at every later time. The evolution is smooth and deterministic. For a single particle, the Hamiltonian is the second line: kinetic energy plus potential energy.

What the wavefunction means came from Max Born, also in 1926. Its squared size gives probabilities, the third line: the chance of finding the particle in a small region. The equation predicts those odds exactly; it does not say which result a single measurement will give.

So I EVOLVE. YOU OBSERVE. is a fair summary. Between measurements, Psykat follows the equation without any randomness at all. At a measurement, one outcome appears, with Born's probabilities. How those two rules fit together is still argued among interpretations of quantum mechanics; the predictions are not in dispute.

Psykat never decides in advance. The equation keeps every possibility moving until someone asks.

Equations

\[i\hbar\,\frac{\partial\Psi}{\partial t} = \hat H\,\Psi\]
\[\hat H = -\frac{\hbar^{2}}{2m}\nabla^{2} + V\]
\[dP = \lvert\Psi\rvert^{2}\,d^{3}r\]
SymbolMeaningUnit
\(\Psi\) wavefunction of one particle in 3-D \(\mathrm{m^{-3/2}}\)
\(i\) imaginary unit \(\mathrm{1}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(t\) time \(\mathrm{s}\)
\(\hat H\) Hamiltonian (energy operator) \(\mathrm{J}\)
\(m\) particle mass \(\mathrm{kg}\)
\(\nabla^{2}\) Laplacian (second derivatives in space) \(\mathrm{m^{-2}}\)
\(V\) potential energy \(\mathrm{J}\)
\(dP\) probability of finding the particle in the small volume d^3r \(\mathrm{1}\)
\(d^{3}r\) small volume element \(\mathrm{m³}\)

Sources

  1. Schrödinger (1926) Quantisierung als Eigenwertproblem (Vierte Mitteilung), Ann. Phys. 386, 109
  2. Born (1926) Zur Quantenmechanik der Stoßvorgänge, Z. Phys. 37, 863
  3. HyperPhysics — Schrödinger Equation
  4. NobelPrize.org — The Nobel Prize in Physics 1933 (Schrödinger, Dirac)
  5. NobelPrize.org — The Nobel Prize in Physics 1954 (Born, Bothe)

Source Schrödinger, E. (1926). Quantisierung als Eigenwertproblem. Annalen der Physik 386, 109–139.doi.org/10.1002/andp.19263861802

Field notes

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