Physics · University
Infinite-well energy ratio · formula reference
A one-dimensional infinite well has n=1,2,...; this question changes quantum number and well width.
Formula
A one-dimensional infinite well has n=1,2,...; this question changes quantum number and well width.
En ∝ n²/L²
Worked example
For the same particle in ideal infinite wells, compare state n=8 at width 3L with state n=9 at width L. Find E(8,3L)/E(9,L). Round the final result to 4 decimal places if needed.
The mass and constants cancel. The ratio is (8²/3²)/9².
0.0878
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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