Potential function for the Time-Independent Schrodinger eq.

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.
  • #1
xago
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Homework Statement



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

Homework Equations



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

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!
 
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  • #2
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.
 

Related to Potential function for the Time-Independent Schrodinger eq.

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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