# Potential function for the Time-Independent Schrodinger eq.

• xago
In summary, the homework problem involves finding solutions to the Time Independent Schrodinger Equation with a potential function and includes transcendental functions in the solutions.
xago

## Homework Statement

[PLAIN]http://img820.imageshack.us/img820/4205/agvg.png

## Homework Equations

TISE: $$\left(-\frac{\hbar}{2m}\nabla^2 + V(r) \right) \psi(r) = E\psi(r)$$

## The Attempt at a Solution

Can someone tell me what 'transcendental' means in part b). I've looked up definitions of the word but I can't see how it applies to the question. If anyone could re-phrase the question or give me some direction that would be great!

Last edited by a moderator:
Transcendental here is just referring to the fact that the equation is going to involve exponential functions. A transcendental function is one that can't be written in terms of finite polynomials.

## 1. What is the Time-Independent Schrodinger equation?

The Time-Independent Schrodinger equation is a fundamental equation in quantum mechanics that describes the behavior of a quantum system. It is a partial differential equation that relates the energy of a system to its wave function.

## 2. Why is a potential function needed in the Time-Independent Schrodinger equation?

The potential function in the Time-Independent Schrodinger equation represents the influence of the external forces on the quantum system. It allows us to consider the effects of the environment on the behavior of the system.

## 3. What is the role of the potential function in determining the energy of a system?

The potential function plays a crucial role in determining the energy levels of a system. It affects the shape and behavior of the wave function, which in turn determines the allowed energy states of the system.

## 4. How is the potential function related to the Hamiltonian operator?

The Hamiltonian operator, which represents the total energy of a system, is directly related to the potential function in the Time-Independent Schrodinger equation. The potential function is multiplied by the wave function in the equation, and the resulting product is used to calculate the energy of the system.

## 5. Can the potential function change over time in the Time-Independent Schrodinger equation?

No, the Time-Independent Schrodinger equation assumes that the potential function is constant over time. This allows us to solve for the energy levels and wave function of a system at a specific time without having to consider the time evolution of the potential function.

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