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Particle in a Box: the Lowest Energy Level of a Particle

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Particle in a box: 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:

Contingency Blocking

A phenomenon in classical conditioning where a previously learned association prevents the acquisition of a new association because the first stimulus is a better predictor of the outcome.

Response Generalization

The process by which a conditioned response is made in reaction to stimuli that are similar to the original conditioned stimulus.

Learned Helplessness

Learned helplessness is a condition in which a person suffers from a sense of powerlessness, arising from a traumatic event or persistent failure to succeed, leading to a belief that one's actions have no effect on the outcome.

Domestic Abuse

Patterns of abusive behavior by one partner towards another in an intimate relationship, including physical, sexual, emotional abuse, and financial control.

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