Why introduce matrix in quantum mechanics

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SUMMARY

The introduction of matrices in quantum mechanics (QM) is essential for transforming state vectors, which represent quantum states. Matrices facilitate operations such as measuring spin through observables like spin operators. This mathematical framework is rooted in linear algebra, where matrices correspond to linear transformations within vector spaces. Understanding these concepts is crucial for solving quantum mechanical problems effectively.

PREREQUISITES
  • Linear algebra fundamentals, including vector spaces and transformations
  • Understanding of quantum mechanics principles, particularly state vectors
  • Familiarity with observables in quantum mechanics, such as spin operators
  • Basic knowledge of matrix operations and their applications in physics
NEXT STEPS
  • Study linear algebra, focusing on vector spaces and matrix transformations
  • Explore the role of observables in quantum mechanics, specifically spin measurements
  • Learn about the mathematical representation of quantum states using state vectors
  • Investigate practical applications of matrices in quantum mechanics through problem-solving
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics, as well as mathematicians interested in the application of linear algebra in physical theories.

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hello,ereryone.I am a senior in china...
Someone asked me this question,and suddlenly i have no idea.
Please,give me some help.
thank!
 
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Because it helps solve problems.
 
Its a natural part of a vector space's structure and associated linear transformations as any book on linear algebra will attest to. Same in QM, since its underlying space of states forms a vector space.

Thanks
Bill
 
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A matrix is a way to transform a vector into another vector. For example, it can rotate a vector. In QM a state vector is used to represent Quantum State so if you want to operate on that state (measure spin for example) you can use a particular type of matrix (an observable such as a spin operator) to operate on the spin state vector. Using this you can determine the measured state, and probabilities.
 

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