Operation on complex conjugate

In summary, sandwiching operators in quantum mechanics is done in a specific way to ensure consistency and avoid the possibility of sending information faster than light by only allowing operators to act on the wavefunction and not its complex conjugate. This is in line with the mathematician's definition of an inner product.
  • #1
Thejas15101998
43
1
Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?
 
Physics news on Phys.org
  • #2
Thejas15101998 said:
Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?

You could define things the other way round. In fact, using the "mathematician's" definition of an inner product would probably have things that way round. All the results would be the same.

See, for example:

https://en.wikipedia.org/wiki/Inner_product_space
 
  • #3
As a follow-up on what PeroK said, note that it is important that you can only do one. If you can operate on a wavefunction and also on that wavefunction's conjugate (or, equivalently, if you're given an operation that can conjugate the wavefunction), it becomes possible to send information faster than light.
 

What is a complex conjugate?

A complex conjugate is a pair of complex numbers where the real parts are the same, but the imaginary parts have opposite signs.

Why are complex conjugates important in mathematics?

Complex conjugates are important because they allow us to simplify complex numbers and perform operations such as division and finding roots.

How do you find the complex conjugate of a given number?

To find the complex conjugate of a given number, simply change the sign of the imaginary part. For example, the complex conjugate of 3+4i is 3-4i.

What is the relationship between a complex number and its complex conjugate?

The relationship between a complex number and its complex conjugate is that when multiplied together, they result in a real number. This is known as the conjugate pair property.

How do you perform operations on complex conjugates?

To perform operations on complex conjugates, simply distribute the operation to both the real and imaginary parts separately, and then combine like terms. For example, to add 3+4i and 5-2i, we add the real parts (3+5=8) and the imaginary parts (4-2=2) to get 8+2i.

Similar threads

Replies
7
Views
642
  • Quantum Physics
Replies
14
Views
2K
  • Precalculus Mathematics Homework Help
Replies
9
Views
334
  • Quantum Physics
Replies
6
Views
2K
  • Quantum Physics
Replies
12
Views
6K
  • Quantum Physics
Replies
17
Views
2K
Replies
28
Views
2K
Replies
25
Views
8K
Replies
15
Views
2K
Replies
5
Views
1K
Back
Top