A particle experiences a potential energy given by U (x) = (x2 – 3)e- x^2

AI Thread Summary
The potential energy function U(x) = (x² - 3)e^(-x²) defines the energy landscape for a particle. To determine the maximum energy for the particle to remain bound, one must analyze the potential energy's behavior, particularly its minima and maxima. For part b, the discussion focuses on the conditions that allow the particle to remain bound for an extended time, which involves understanding the stability of the potential well. The possibility of the particle having energy greater than that in part b while still being temporarily bound is also explored, emphasizing the transient nature of such states. Overall, the thread seeks guidance on how to approach these questions using relevant equations and concepts.
acusanelli
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Homework Statement



A particle experiences a potential energy given by

U (x) = (x2 – 3)e- x^2

a) . What is the maximum energy the particle could have and yet be bound?

b) What is the maximum energy the particle could have and yet be bound for a considerable length of time?

c) Is it possible for the particle to have an energy greater than that in part b) and still be “bound” for some period of time? Explain.

The Attempt at a Solution



dont know where to start and would like some help. maybe some equations or just help with guiding me along. thank you
 
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