How is Schrodinger equation applied to particles in a box?
The idealized situation of a particle in a box with infinitely high walls is an application of the Schrodinger equation which yields some insights into particle confinement. The wavefunction must be zero at the walls and the solution for the wavefunction yields just sine waves.
What is meant by perturbation theory?
Definition of perturbation theory : any of various methods of calculating the approximate value of a complex function (such as the energy of an electron in quantum mechanics) by first assuming that the dominant influence is the only factor and then making small corrections for additional factors.
What is the particle in a box theory?
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. Likewise, it can never have zero energy, meaning that the particle can never “sit still”.
What is perturbation theory and why we use this theory?
Perturbation theory is a method for continuously improving a previously obtained approximate solution to a problem, and it is an important and general method for finding approximate solutions to the Schrödinger equation. We discussed a simple application of the perturbation technique previously with the Zeeman effect.
What is the significance of particle in a box solution?
Introduction. The particle in a box problem is a common application of a quantum mechanical model to a simplified system consisting of a particle moving horizontally within an infinitely deep well from which it cannot escape. The solutions to the problem give possible values of E and ψ that the particle can possess.
What are the most likely locations of a particle in a box?
The most probable position is where the square of the wave function has the largest value. The mathematical way of answering this question is to integrate the square of the wave function, times the quantity of interest x, over the entire box.