# Initial condition of Wave functions with Yukawa Potential

• Riccardo Marinelli
In summary, the conversation discusses finding eigenfunctions of the Schrödinger equation with Yukawa potential and the boundary conditions for the eigenfunctions. The individual is unsure if the boundary conditions are the same as those for Coulomb potential, and asks for recommendations for further information if they are wrong. The provided potential equation is also acknowledged.

#### Riccardo Marinelli

Homework Statement
Find eigenfunctions of Schrödinger equation with Yukawa potential
Relevant Equations
$$V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$$
Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1, am I right or have I to be more careful?
In the case I'm wrong do you know some articles or books where I can find some information about these conditions?

Last edited:
correct and the wave function needs to go to $0$ as $r \rightarrow \infty$

Yes, in order to find the eigenvalue I impose that the wavefunction goes to zero, thank you

Riccardo Marinelli said:
Homework Statement:: Find eigenfunctions of Schrödinger equation with Yukawa potential
Relevant Equations:: $V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$

Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1, am I right or have I to be more careful?
In the case I'm wrong do you know some articles or books where I can find some information about these conditions?

You're a couple of dollars short there:
$$V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$$

TSny and Riccardo Marinelli
Thank You ! I was wondering how to insert Latex properly!

## 1. What is the initial condition for a wave function with Yukawa potential?

The initial condition for a wave function with Yukawa potential is the value of the wave function at the starting point of the potential. This can be represented as ψ(x=0) or ψ(0).

## 2. How is the initial condition of a wave function with Yukawa potential determined?

The initial condition of a wave function with Yukawa potential is determined by solving the Schrödinger equation for the specific potential and applying boundary conditions. This will give the value of the wave function at the starting point of the potential.

## 3. Can the initial condition of a wave function with Yukawa potential be negative?

Yes, the initial condition of a wave function with Yukawa potential can be negative. The wave function is a complex quantity and can have both real and imaginary components. The initial condition is determined by the value of the wave function at a specific point and can be positive, negative, or zero.

## 4. Does the initial condition of a wave function with Yukawa potential affect its behavior?

Yes, the initial condition of a wave function with Yukawa potential can significantly affect its behavior. The initial condition determines the starting point of the wave function and can influence the amplitude, phase, and shape of the wave function as it propagates through the potential.

## 5. Can the initial condition of a wave function with Yukawa potential change over time?

No, the initial condition of a wave function with Yukawa potential remains constant over time. The wave function may change as it propagates through the potential, but the initial condition remains the same. However, the initial condition can be adjusted by changing the starting point of the potential or by applying external forces to the system.