Schrödinger Equation: Solving for Energy in a Semi-Infinite Square Well"

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SUMMARY

The discussion focuses on solving the Schrödinger equation for a semi-infinite square well, specifically addressing the calculation of energy levels. The participant correctly identifies the relationship between wave number (K) and energy (E) using the formula E = (K^2 • h^2)/(2m), where h is Planck's constant (6.626 x 10^-34 J•s). The participant also notes the requirement for continuity of the wave function and its derivative at the boundary (X=L), indicating a solid understanding of the boundary conditions necessary for this problem.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with quantum mechanics concepts, specifically potential wells
  • Knowledge of boundary conditions in wave functions
  • Basic proficiency in algebra and calculus for solving equations
NEXT STEPS
  • Study the derivation of energy levels in a semi-infinite square well
  • Learn about boundary conditions and their implications in quantum mechanics
  • Explore the concept of wave functions and normalization in quantum systems
  • Investigate the role of Planck's constant in quantum mechanics calculations
USEFUL FOR

Students of advanced physics, particularly those studying quantum mechanics and wave functions, as well as educators and researchers looking to deepen their understanding of potential wells and energy quantization.

Ashley1nOnly
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Homework Statement


I have an attachment

Homework Equations


Schrödinger equation

The Attempt at a Solution


The issues I am having is how to start this one. This is not a infinite square well but a semi-infinite square well.
I know that energy= K^2= 2mE/h^2
Where h is planks constant 6.626 X 10^-34 J•s
So rearranging (K^2 • h^2)/(2m) =E
How do I find my m and solve the other ones

At X=L
The first derivatives must be equal at X=L
Asin(kL)=Ce^(-aL)
KAcos(kL)=-aCe^(-aL)

Am I going in the right direction
 
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