Chapter 1: Problem 13

What is eigen function and what is its significance?

Short Answer

Expert verified

Eigenfunctions are functions that under the action of an operator, return the original function times a constant. They are crucial in understanding quantum mechanics as they denote the various states of a physical system.

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Definition of an Eigenfunction

An eigenfunction of a given operator is a function that, under the action of that operator, returns a constant (the eigenvalue) times the original function. More formally, we can express this as if \( \hat{O} \) is an operator and \( \psi \) is its eigenfunction, then \( \hat{O}\psi = \lambda\psi \), where \( \lambda \) is the eigenvalue.

Significance of Eigenfunctions

Eigenfunctions are of prime importance in many areas of physics, especially quantum mechanics. The eigenfunctions describe the different states a physical system may be in. The concept of eigenfunctions and eigenvalues is crucial to understand the behavior of particles in quantum mechanics which is why their values help in predicting measurable quantities or the properties of physical systems. Quantum states are often described by eigenfunctions of operator equations, and observing a quantum system will cause it to jump to an eigenstate of the operator corresponding to the observed quantity.

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What is eigen function and what is its significance?

Short Answer

Step by step solution

Definition of an Eigenfunction

Significance of Eigenfunctions

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