Solving for constants given boundary conditions

In summary, boundary conditions are values or constraints used to solve for unknown constants in a mathematical equation or system. It is important to solve for constants given boundary conditions in order to accurately model and understand a system. The process of solving for constants involves using known boundary conditions and mathematical techniques to determine the values of the constants. Boundary conditions can be changed or adjusted in certain situations. However, there are limitations to using boundary conditions, such as the possibility of inaccurate or incomplete solutions and the difficulty of determining unique solutions for certain equations or systems.
  • #1
xago
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Homework Statement



[PLAIN]http://img843.imageshack.us/img843/3515/11193469.png


Homework Equations





The Attempt at a Solution



[PLAIN]http://img801.imageshack.us/img801/4829/scan0001i.jpg

An upload of my attempt to solve the problem. Not sure to interpret the results.
A = B = 0
C = -C*
C = Ce-2ikL
 
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  • #2
That's not quite right. There can be other values of k for which sin(kL)=0. This means that B is not necessarily zero. Hence solve the equation sin(kL)=0 for k.
After this to get the B you have to normalize the wavefunction.
 

FAQ: Solving for constants given boundary conditions

1. What are boundary conditions in the context of solving for constants?

Boundary conditions refer to the specific values or constraints that are used to solve for unknown constants in a mathematical equation or system. These conditions can include initial conditions, specific points or values, or other known information that helps determine the value of the constants.

2. Why is it important to solve for constants given boundary conditions?

Solving for constants allows us to fully understand and accurately model a system or phenomenon. By using boundary conditions, we can determine the specific values of constants that will accurately predict the behavior of the system. This is crucial in many scientific fields, such as engineering, physics, and chemistry.

3. How do you solve for constants given boundary conditions?

The process of solving for constants varies depending on the specific equation or system being analyzed. However, in general, it involves setting up the equation or system with the known boundary conditions and then using mathematical techniques, such as substitution or integration, to solve for the unknown constants.

4. Can boundary conditions ever be changed or adjusted?

Yes, boundary conditions can be changed or adjusted in certain situations. This can happen if new information is discovered that affects the behavior of the system, or if the system itself changes over time. In these cases, the constants may need to be recalculated using the updated boundary conditions.

5. Are there any limitations to using boundary conditions to solve for constants?

There are some limitations to using boundary conditions to solve for constants. In some cases, the boundary conditions may not fully capture the complexity of the system, leading to inaccurate or incomplete solutions. Additionally, certain types of equations or systems may not have unique solutions, making it difficult to determine the values of the constants.

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