Of course, this is not done automatically you must do the work, or remember to use this operator properly in algebraic manipulations. 3.4: Operators, Eigenfunctions, Eigenvalues, and Eigenstates he Laplacian operator is called an operator because it does something to the function that follows: namely, it produces or generates the sum of the three second-derivatives of the function.In order to reach this objective, we need the appropriate wave equation. 3.3: Invention of the Schrödinger Equation Our goal as chemists is to seek a method for finding the wavefunctions that are appropriate for describing electrons, atoms, and molecules.
We will consider a sine wave, take its first and second derivatives, and then examine the results. 3.2: A Classical Wave Equation The easiest way to find a differential equation that will provide wavefunctions as solutions is to start with a wavefunction and work backwards.Such thoughts may have motivated Erwin Schrödinger to argue that the wave equation is a key component of Quantum Mechanics. This differential equation is called the wave equation, and the solution is called the wavefunction. 3.1: Introduction to the Schrödinger Equation The Schrödinger equation is the fundamental postulate of Quantum Mechanics.If electrons, atoms, and molecules have wave-like properties, then there must be a mathematical function that is the solution to a differential equation that describes electrons, atoms, and molecules.