# Why did Schrodinger call his equation eigenvalue problem?

• kahoomann
In summary, Schrodinger called his equation an eigenvalue problem because it can be written as a separable PDE, generating ODEs in the form of Sturm-Liouville differential equations. It is similar to the concept of eigenvalues in linear algebra, where the operator acts on a function and the eigenvalue is introduced as a separation constant. The equation is also known as an eigenvalue equation, with H representing the total energy and E as the energy eigenvalue.
kahoomann
Why did Schrodinger call his equation eigenvalue problem?
We can solve Schrodinger equation since it's just differential equation with complex number

The Schrodinger equation is a separable PDE, and in separating the PDE you generate ODEs which are of the form of Sturm-Liouville differential Equations:

http://en.wikipedia.org/wiki/Sturm-Liouville_theory

Basically what the separated equations look like is

$$\mathcal{L}u = \lambda u$$

where $\mathcal{L}$ is a linear differential operator acting on the function u and $\lambda$ is the eigenvalue, which is the separation constant introduced from separating the PDE. This is just a generalization, if you like, of the case in linear algebra, where the operator would be a matrix and u would be a vector. One difference between the two cases is that in linear algebra the eigenvalue spectrum is finite, whereas in the Sturm-Liouville theory it is generally infinite.

eigen value problem

Dear friend i don't know much of physics,but to me,its called eigen value equation bcoz we can write it in simple form as
H(psi) = E(psi)
H being hamiltonian or total energy of system,and E being energy eigen value.

## 1. Why did Schrodinger use the term "eigenvalue" in his equation?

Schrodinger used the term "eigenvalue" because it refers to a set of special numbers that describe the possible energy levels of a quantum system. These values are unique to each system and are independent of the observer, making them "eigen" or self-values.

## 2. What is the significance of an "eigenvalue problem" in Schrodinger's equation?

An "eigenvalue problem" in Schrodinger's equation refers to the mathematical process of finding the eigenvalues and corresponding eigenfunctions of the system. This allows scientists to understand and predict the behavior of quantum systems.

## 3. How does Schrodinger's equation relate to the concept of superposition?

Schrodinger's equation describes the motion and behavior of a quantum system, including the possibility of superposition. This means that a system can exist in multiple states simultaneously, until it is observed and collapses into a single state.

## 4. Was Schrodinger the first person to use the term "eigenvalue" in physics?

No, Schrodinger was not the first person to use the term "eigenvalue" in physics. The concept of eigenvalues was first introduced by mathematician David Hilbert in 1904, but it was Schrodinger who applied this concept to quantum mechanics in his famous equation.

## 5. How did Schrodinger's equation impact the development of quantum mechanics?

Schrodinger's equation is considered one of the most important and influential equations in quantum mechanics. It helped to unify and explain many different phenomena in the quantum world, and it continues to be a fundamental tool in studying and understanding quantum systems.

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