Operators in Quantum Mechanics

[shyjuu]

I am not able to understand exactly why operators are required in Quantum Theory, what is its use

 

According me its like normal + - * and / operator used in mathematics .

for example a+b = some value, so here + is an operator,

so I want know is the operator used in Quantum Theory also the same,does it work in same manner how it is different

 

Thanks a lot in advance for replies

[swansont]

Operators can also include things like a gradient or Laplacian.

 

The concept here is that what are values in classical mechanics are operators in QM. Rather than finding momentum by taking mass x velocity and getting a number, you get it by applying the momentum operator on the wave function, and the result gives you an equation. [math]P\Psi = p\Psi[/math] where P is the operator, [math]-i\hbar\nabla[/math] and p is the momentum. From this you can determine momentum eigenvalues.

[John Cuthber]

You do things like add and divide or sin(x) with numbers.

Operators act on functions, rather than on numbers.

Edited November 10, 2013 by John Cuthber

[studiot]

Shyjuu

According me its like normal + - * and / operator used in mathematics .

for example a+b = some value, so here + is an operator,

 

John Cuthber

You do things like add and divide or sin(x) with numbers.

Operators act on functions, rather than on numbers.

 

Yes +,-,* & / are operators but operators have a pretty wide ranging definition and include operators on numbers.

 

They are like but their definition is even wider than functions since some allow multiple outputs or results, unlike functions.

An example here might be the square root extraction operator that can return either the positive or negative square root.

 

Most operators require an argument or operand to operate on but there is even a class of operator that doe not take an argument. These are called nullary or niladic operators.

 

Examples of these are the end, exit and void statements in programming.

 

Other interesting operators are the rotation operator, the negation operator, the complementation operator. The rotation operator has a place in QM.