---
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 solve and says what its answer, a wavefunction, does and does not tell you about an ele"
canonical: https://lightmysky.com/learn/science/the-schrodinger-equation-and-what-a-wavefunction-says-mt_WCwbaO9rpR
source: https://lightmysky.com/learn/science/the-schrodinger-equation-and-what-a-wavefunction-says-mt_WCwbaO9rpR.md
retrieved: 2026-09-12
---

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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 solve 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 is a solution of one equation. It says a kinetic term plus a potential term, acting on the wavefunction, gives the energy times the wavefunction. Only certain wavefunctions fit a given atom, and each allowed one carries its own fixed energy. That selectiveness is where quantised energies come from.

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 is always a real probability. 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 that 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. One broken rule is enough to throw the whole candidate out.

**Tip.** 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

- [Energy Levels and Line Spectra](https://lightmysky.com/learn/science/energy-levels-and-line-spectra-mt_RlMCSDxE5q)
- [Orbitals, Sub-Shells and Electron Configuration](https://lightmysky.com/learn/science/orbitals-sub-shells-and-electron-configuration-mt_sRMo1f5PfJ)
- [Stationary Points and the Second Derivative](https://lightmysky.com/learn/mathematics/stationary-points-and-the-second-derivative-mt_VbGJEFFgfs)
- [de Broglie Waves and Electron Diffraction](https://lightmysky.com/learn/science/de-broglie-waves-and-electron-diffraction-mt_Y8NthsmPcv)

## 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)