Quantum mechanics, vectorrepresentation

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Homework Help Overview

The discussion revolves around a quantum mechanics problem involving a vector representation of a function with constants. The original poster is seeking guidance on how to determine the constants in the given vector expression and whether additional information is needed.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the normalization condition of the vector and its implications for finding the constants. The original poster questions the sufficiency of the provided information and considers the relevance of eigenvalues and eigenvectors from the Jy-matrix.

Discussion Status

The conversation is ongoing, with some participants noting that the normalization condition alone does not yield unique solutions. The original poster is exploring potential connections to other quantum mechanical concepts, indicating a search for a more comprehensive understanding.

Contextual Notes

There is mention of specific operators (J+, J-, Jz) and their associated eigenvalues and eigenvectors, suggesting that these may play a role in the original poster's approach to the problem. However, the exact relationship to the constants remains unclear.

Kentaxel
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Homework Statement



For the function

[itex]\chi^{(y)}=c_{1}<br /> <br /> \left( \begin{array}{ccc}<br /> -1\\<br /> i\sqrt{2}\\<br /> 1\end{array} \right)<br /> +<br /> <br /> c_{2}<br /> <br /> \left( \begin{array}{ccc}<br /> 1\\<br /> 0\\<br /> 1\end{array} \right)<br /> +<br /> c_{3}<br /> <br /> \left( \begin{array}{ccc}<br /> -1\\<br /> -i\sqrt{2}\\<br /> 1\end{array} \right)[/itex]

how would i go on about finding the constants, is this enough information or is something missing?
 
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The only condition on the vector is to be normalized. This won't provide you with nothing but a condition involving all 3 constants altogether. There is an infinite number of solutions.
 
So what do i need to find them? I got the vectors from the Jy-matrix and its eigenvalues, could i use this somehow? I also know J+, J-, Jz and the eigenvectors/values for the (chi)z, could this be usefull? I can't figure out how to put it together but the full solution requires a normalized vector.
 
Solution to what?
 

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