HackaB said:This thread, https://www.physicsforums.com/showthread.php?t=74810, was orignally posted here in the QM forum, but it was moved to the homework section, which is reasonable. But nobody there knows quantum mechanics.
ZapperZ said:What do you mean that nobody there knows quantum mechanics?
There were several responses, and from what I've seen, I certainly cannot say that those responders did not know QM.
The problem isn't easy due to the projection operator as its potential. You need someone willing to grind it out to work through this. It has nothing to do with people not knowing QM. Almost everyone who reads this section also read the Homework section.
Zz.
An eigenvalue is a scalar value that represents the magnitude of a specific property of a mathematical object, such as a matrix or operator. In physics, eigenvalues are often used to describe the energy levels of quantum systems.
Finding eigenvalues allows us to understand the properties and behavior of a mathematical object. In physics, eigenvalues are particularly important because they can help us solve problems related to quantum mechanics and understand the behavior of complex systems.
The process of finding eigenvalues involves solving a special type of equation known as the characteristic equation. This equation is obtained by setting the determinant of the matrix or operator equal to zero. Once the characteristic equation is solved, the solutions are the eigenvalues.
Eigenvalues and eigenvectors are closely related. Eigenvectors are the corresponding vectors that represent the direction of the special property associated with the eigenvalue. In physics, eigenvectors are often used to describe the states of a quantum system.
Yes, eigenvalues can be complex numbers. In quantum mechanics, complex eigenvalues often arise when describing systems with time-dependent behavior. They can also be used to describe systems with periodic behavior, such as a quantum oscillator.