Operators in quantum mechanics

In summary, the speaker is a newcomer who has completed their BS in physics and is now pursuing a M.Sc in quantum mechanics. They are looking for recommendations for a book on linear operators in quantum mechanics and mention that they have struggled with algebra and functional spaces. Another speaker suggests Reed and Simon's "Methods of modern mathematical physics" and another recommends Von Neumann's book. Additionally, they mention that having a good understanding of complex analysis and probability will be helpful in their studies.
  • #1
Atanu
1
0
I'm a newcomer here... so I introduce myself:
I've just completed my BS in physics and joining M.Sc... I've interested to take specialisation in Quantum mechanics and will continue in theoretical physics in the future...

I'm facing problems understanding the algebra of operators... basically realting the functional spaces... can anyone please suggest me the finest and the easiyest book on "Linear operators in quantum mechanics"..
I'll be greatful...
 
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  • #2
I'd definitely take a look at:

Reed M., Simon B. Methods of modern mathematical physics, v.1-4
 
  • #3
It's a fair bit dated, but I quited enjoyed Von Neumann's book.
 
  • #4
Yes I would agree that von Neumann's book is a quite good mathematical introduction.
 
  • #5
a good understanding of complex analysis and probability will also help in your QM studies
 

Related to Operators in quantum mechanics

1. What are operators in quantum mechanics?

Operators in quantum mechanics are mathematical objects that act on quantum states to produce new quantum states. They are used to represent physical observables, such as position, momentum, and energy, and are essential for describing the behavior of quantum systems.

2. How are operators represented in quantum mechanics?

In quantum mechanics, operators are typically represented by matrices. Each element of the matrix corresponds to a specific operation on the quantum state. For example, a position operator might be represented by a matrix with elements that correspond to the position of the particle in different dimensions.

3. What is the role of operators in determining the state of a quantum system?

Operators play a crucial role in determining the state of a quantum system. By applying operators to a given quantum state, we can calculate the probability of obtaining a particular measurement result. This allows us to make predictions about the behavior of quantum systems.

4. Can operators in quantum mechanics be measured?

No, operators themselves cannot be measured directly. Instead, they are used to represent physical observables that can be measured. The measurement process involves applying an operator to a quantum state and obtaining a measurement result, which corresponds to an eigenvalue of the operator.

5. How do operators in quantum mechanics relate to classical mechanics?

Operators in quantum mechanics have a direct correspondence to observables in classical mechanics. However, in quantum mechanics, the operators are represented by matrices, whereas in classical mechanics, observables are represented by functions. This is one of the fundamental differences between the two theories.

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