Solving Potential Homework: 6 Eqns, 6 Unknwns & 7 Eqns, 7 Unknwns

In summary, the conversation is about a question regarding a potential where the R and T coefficients do not add up to one for E < V0, despite there being six equations and six unknowns. The individual has tried solving it in different ways but still cannot get R + T = 1. They mention a harder case for E > V0 with seven unknowns and six equations. They also mention using continuity requirements and potentially changing the interior wavefunctions into sine/cosine forms to reduce the number of unknowns when matching at zero.
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splitringtail
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Homework Statement




I have a question concerning this potential. For E < V0, I have the R and T coefficients, but there sum doesn't equal one, but you have six equations and six unknowns, so its easy to solve I guess.. I have gotten the same answers doing it different ways but can't seem to get R+T=1.

However, it is a lot easier case then solving the case for when E > V0 I have seven unknowns and six equations.

All these equations I have gotten from the continuity requirements. Could I be missing something else?


Could I at least change the interior wavefuntions into sine/cosine since the exponent forms since it's reduces unknowns when matching at zero?

Homework Equations





The Attempt at a Solution

 

Attachments

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What are the equations and unknowns involved in this homework?

The first set of equations involves 6 equations and 6 unknowns, while the second set has 7 equations and 7 unknowns. The unknowns refer to the variables that need to be solved for in each equation.

How do I solve for multiple unknowns in an equation?

In order to solve for multiple unknowns in an equation, you will need to use a method such as substitution or elimination. These methods involve manipulating the equations to isolate one unknown at a time and then substituting the value into the other equations.

What are some common mistakes to avoid when solving these types of equations?

Some common mistakes to avoid include forgetting to distribute negative signs, mixing up the order of operations, and making arithmetic errors. It is also important to check your final answers for accuracy and to make sure they satisfy all of the given equations.

What are some tips for solving these equations efficiently?

One tip is to first identify which method (substitution or elimination) will be most efficient for solving the equations. Another tip is to always double-check your work and to use a calculator if necessary. It can also be helpful to start by solving for the simplest unknowns first.

How can I check my answers to ensure they are correct?

You can check your answers by plugging them into each of the original equations and making sure they satisfy all of them. Another way to check is by graphing the equations and seeing if the solution point aligns with the intersection of all the lines. Additionally, you can ask a classmate or teacher to review your work and provide feedback.

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