Why introduce matrix in quantum mechanics

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Discussion Overview

The discussion centers around the role of matrices in quantum mechanics, exploring their significance in relation to vector spaces and linear transformations. Participants seek to understand why matrices are introduced in the context of quantum states and measurements.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that matrices help solve problems in quantum mechanics.
  • Another participant explains that matrices are a natural part of the structure of vector spaces and linear transformations, which is also applicable in quantum mechanics due to the vector space of states.
  • A further contribution describes matrices as tools to transform state vectors, specifically mentioning their role in operations like measuring spin states using observables.

Areas of Agreement / Disagreement

Participants present various perspectives on the introduction of matrices in quantum mechanics, but there is no explicit consensus on a singular reason or explanation.

Contextual Notes

The discussion does not address specific assumptions or limitations regarding the definitions of matrices or vector spaces in quantum mechanics.

Who May Find This Useful

Students and individuals interested in the foundational concepts of quantum mechanics, particularly those exploring the mathematical structures involved.

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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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