Why introduce matrix in quantum mechanics

[qls]

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!

 

[dauto]

Because it helps solve problems.

 

[bhobba]

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

 

[meBigGuy]

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.