Is A a Linear Operator and Hermitian in Quantum Mechanics Postulate 2?

In summary, the conversation is about the superposition principle in quantum mechanics. The person is having trouble with a specific problem involving the operator A and is seeking clarification on whether it is a linear operator and a Hermitian. They later figure out how to solve the problem and receive a tip on using proper notation to better understand mathematical operations.
  • #1
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Hi I am new here and also new to QM.

I have encountered a problem about postulate 2 which is the superposition principle. Basically I understand the concept. However, when it comes to real question, I get stuck and can't proceed. Could anyone enlightens me how to get started with the problem below?

Question:
A psi(x) = [psi(x)]^2

Is A a linear operator? Is A a Hermitian?
 
Last edited:
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  • #2
Heh, I found the way to solve it already! :smile:
 
  • #3
BTW: You should start using the notation [tex](A\psi )(x)[/tex] instead of [tex]A\,\psi(x)[/tex]. It will help you to understand better the mathematical operations involved.

[tex](A\psi )(x)[/tex] reads: the value of the function [tex]A\psi[/tex] at the point x.

Operators act on functions (as objects) and not on values of these functions (numbers).
 

FAQ: Is A a Linear Operator and Hermitian in Quantum Mechanics Postulate 2?

What is the postulate of quantum mechanics?

The postulate of quantum mechanics states that the state of a quantum system is described by a wave function, and the evolution of this wave function is governed by the Schrödinger equation.

How does the postulate of quantum mechanics differ from classical mechanics?

The postulate of quantum mechanics differs from classical mechanics in that it allows for the superposition of states, where a quantum object can exist in multiple states simultaneously. In classical mechanics, an object can only be in one state at a time.

Can the postulate of quantum mechanics be proven?

No, the postulate of quantum mechanics cannot be proven. It is a fundamental principle that has been extensively tested and has been found to accurately describe the behavior of quantum systems.

Are there any limitations to the postulate of quantum mechanics?

While the postulate of quantum mechanics has been incredibly successful in predicting the behavior of microscopic systems, it does have limitations when it comes to describing macroscopic objects. It also cannot fully explain the phenomenon of gravity.

How has the postulate of quantum mechanics impacted our understanding of the universe?

The postulate of quantum mechanics has revolutionized our understanding of the universe and has led to the development of groundbreaking technologies such as transistors, lasers, and MRI machines. It has also challenged our traditional understanding of reality and has implications for fields such as philosophy and metaphysics.

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