The Lowest Energy Level of a Particle Confined to a One-Dimensional

question 19

Short Answer

The lowest energy level of a particle confined to a one-dimensional region of space (a box,or infinite well)with fixed length L is E₀.If an identical particle is confined to a similar region with fixed length L/6,what is the energy of the lowest energy level that the particles have in common? Express your answer in terms of E₀.

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Definitions:

Factoring

The process of breaking down an expression into simpler terms that, when multiplied together, produce the original expression.

Square Root Property

The square root property states that if \(x^2 = a\), then \(x = \pm\sqrt{a}\), assuming \(a\) is non-negative.

Complex Solutions

Solutions to equations that involve complex numbers, which include a real component and an imaginary component.

Real Solutions

Real solutions refer to the solutions of an equation that are real numbers, as opposed to complex or imaginary numbers.