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SCHRODINGER WAVE FUNCTION HOW TO

To distinguish it from classical, point-like particles, such an object is called a quantum mechanical particle. More exciting is the case, when the particle behaves like a wave. Particle-like behaviour can be described by classical mechanics. This wave function represents a probability of measuringthe particle at a position x at a time t. Imagine we are following the motion of a single particle in onedimension.

The de-Broglie wavelength 2 is also a measure of whether the object behaves more like a particle or a wave. The wave functionpsi is a function of both position x and time t,and is the fundamental description of the realm of the very small. This is how the time-independent Schrödinger equation looks like:

SCHRODINGER WAVE FUNCTION HOW TO

Separation of variables and stationary states Here you will learn how to simplify the solution of the time-dependent Schrödinger equation by variable separation and what the stationary states are.Īfter this lesson, you will understand where the famous Schrödinger equation comes from, what it means, and what you can do with it.

Time-dependent Schrödinger equation (1d and 3d) Here we try to motivate ("derive") the time-dependent Schrödinger equation with a little magic.

With the latter we formulate the Schrödinger equation as an eigenvalue equation.

Time-independent Schrödinger equation (3d) We generalize the one-dimensional Schrödinger equation to the three-dimensional version and encounter the Laplace and Hamilton operator.

Wave function in classically allowed and forbidden regions Here you will learn the general behavior of the wave function in the classically allowed and forbidden regions and the resulting energy quantization.

Squared magnitude, probability and normalization Here you learn the statistical Interpretation of the Schrödinger equation and the associated squared magnitude of the wave function.

Derivation of the time-independent Schrödinger equation (1d) Here the Schrödinger equation is derived with the help of energy conservation, wave-particle dualism and plane wave.

Applications Here you'll learn some technical applications of the Schrodinger equation.

Quantum Mechanics Here classical mechanics is compared with quantum mechanics. It ensures that is a finite number so we can use it to calculate probabilities.Updated by Alexander Fufaev on Table of contents

This third condition follows from Born’s interpretation of quantum mechanics. The third condition requires the wave function be normalizable. (In a more advanced course on quantum mechanics, for example, potential spikes of infinite depth and height are used to model solids). The second condition requires the wave function to be smooth at all points, except in special cases. The first condition avoids sudden jumps or gaps in the wave function. The first derivative of with respect to space,, must be continuous, unless.The time-independent wave function solutions must satisfy three conditions: These cases provide important lessons that can be used to solve more complicated systems. In the next sections, we solve Schrӧdinger’s time-independent equation for three cases: a quantum particle in a box, a simple harmonic oscillator, and a quantum barrier. The wave-function solution to this equation must be multiplied by the time-modulation factor to obtain the time-dependent wave function.

Notice that we use “big psi” for the time-dependent wave function and “little psi” for the time-independent wave function. This equation is called Schrӧdinger’s time-independent equation. Where E is the total energy of the particle (a real number).