How does the potential for Quantum Mechanics differ between two scenarios?

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SUMMARY

The discussion focuses on the differences in potential energy scenarios in quantum mechanics, specifically comparing the infinite potential well defined by V(x)={Inf for x<0, bx for 0a} and V(x)={Inf for x<0, bx for x>0}. Participants analyze how these potentials affect the solutions to Schrödinger's equation, wave functions, and energy states. The key takeaway is that the infinite potential imposes boundary conditions that significantly influence the behavior of wave functions and the quantization of energy levels.

PREREQUISITES
  • Understanding of Schrödinger's equation
  • Familiarity with potential energy functions in quantum mechanics
  • Knowledge of boundary conditions in differential equations
  • Basic concepts of wave functions and energy quantization
NEXT STEPS
  • Research the implications of infinite potential wells in quantum mechanics
  • Study the mathematical treatment of boundary conditions in differential equations
  • Learn about the quantization of energy levels in various potential scenarios
  • Explore the role of wave functions in determining particle behavior in quantum systems
USEFUL FOR

Students and professionals in physics, particularly those specializing in quantum mechanics, as well as educators looking to deepen their understanding of potential energy scenarios and their implications on wave functions and energy states.

ynuo
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How does this potential:

V(x)={Inf for x<0, bx for 0<x<a, Inf for x>a}

differ from:

V(x)={Inf for x<0, bx for x>0}

with regards to Schrödinger's equation, wave functions, and the energy states.

P.S. the tex graphics are not showing when I try to post my question using tex macros. This is why I resorted to plain ascii.
 
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Do you know how to treat an infinite potential within the context of 1-dim SE ?
 
This is the part that I have trouble with. I know that if I had a constant
potential or any other type of potential, then a substitution in Schrödinger's
equation will be required. From there I will have to solve a DE. But in
the case of infinite potential I am not sure.
 
Saying 'infinite potential' specifies a boundary condition for the DE. Guess which one?
 
I think I got it. Thanks.
 

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