---
title: "The Schrodinger Equation and What a Wavefunction Says"
description: "Orbitals have been used as pictures handed down from somewhere else. This stop names the equation those pictures come from, exactly for hydrogen and approximately for atoms with more electrons, and sa"
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source: https://lightmysky.com/learn/science/the-schrodinger-equation-and-what-a-wavefunction-says-mt_WCwbaO9rpR.md
retrieved: 2026-11-12
---

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# The Schrodinger Equation and What a Wavefunction Says

Orbitals have been used as pictures handed down from somewhere else. This stop names the equation those pictures come from, exactly for hydrogen and approximately for atoms with more electrons, and says what its answer, a wavefunction, does and does not tell you about an electron.

Subject: Science · Area: Chemistry · Ages 18 to 19
Page: https://lightmysky.com/learn/science/the-schrodinger-equation-and-what-a-wavefunction-says-mt_WCwbaO9rpR

## Ready when they can

- States the time-independent equation as an energy statement: a kinetic term plus a potential term acting on the wavefunction returns the energy times the wavefunction
- Explains why the square of the wavefunction, not the wavefunction itself, is the measurable quantity
- Lists the conditions a physically acceptable wavefunction has to meet, and rejects a proposed function that breaks one
- Says why an electron in an atom has no path, and what replaces the path in the quantum account

## Lesson: The equation behind every orbital

Every orbital picture you have used comes from one equation, solved exactly for hydrogen's one electron; many-electron atoms need an approximation with one wavefunction per electron. The equation says kinetic plus potential terms acting on the wavefunction give the energy times the wavefunction. Only certain wavefunctions fit, each with a fixed energy, so energies are quantised.

The wavefunction itself is not what you measure. Square it and you get the probability density, which tells you where the electron is likely to be found. The wavefunction can be negative, but its square never is, so the square can serve as a density of odds. Where the square is zero sits a node, and the electron is never found there.

**Example.** Suppose someone hands you a candidate wave that jumps suddenly at one point, or keeps growing far from the nucleus. You reject it. An acceptable wavefunction is continuous, single valued and finite, and it fades to zero far away so the total odds can add up to one. One broken rule is enough to throw it out.

Stop picturing the electron as a dot running on a track. It has no path, only a standing wave pattern around the nucleus. What replaces the path is a set of allowed states, each with a definite energy. Learn to ask which state the electron is in, never where it is heading.

**Recap.** The equation picks the allowed waves, the square gives the odds, and no path is needed.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Orbitals, Sub-Shells and Electron Configuration](https://lightmysky.com/learn/science/orbitals-sub-shells-and-electron-configuration-mt_sRMo1f5PfJ)
- [de Broglie Waves and Electron Diffraction](https://lightmysky.com/learn/science/de-broglie-waves-and-electron-diffraction-mt_Y8NthsmPcv)

## Optional connections

- [Energy Levels and Line Spectra](https://lightmysky.com/learn/science/energy-levels-and-line-spectra-mt_RlMCSDxE5q)
- [Stationary Points and the Second Derivative](https://lightmysky.com/learn/mathematics/stationary-points-and-the-second-derivative-mt_VbGJEFFgfs)

## Opens up

- [The Particle in a Box: Where Quantised Levels Come From](https://lightmysky.com/learn/science/the-particle-in-a-box-where-quantised-levels-come-from-mt_rOCXlEi324)