derive Schrodinger wave equation
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Explanation:
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Explanation:
The Schrödinger equation (also known as Schrödinger’s wave equation) is a partial differential equation that describes the dynamics of quantum mechanical systems via the wave function. The trajectory, the positioning, and the energy of these systems can be retrieved by solving the Schrödinger equation.
All of the information for a subatomic particle is encoded within a wave function. The wave function will satisfy and can be solved by using the Schrodinger equation. The Schrodinger equation is one of the fundamental axioms that are introduced in undergraduate physics. It is also increasingly common to find the Schrödinger equation being introduced within the electrical engineering syllabus in universities as it is applicable to semiconductors.
Unfortunately, it is only stated as a postulate in both cases and never derived in any meaningful way. This is quite dissatisfying as nearly everything else taught in undergraduate quantum physics is built upon this foundation. In this article, we will derive the equation from scratch and I’ll do my best to show every step taken.
Interestingly enough, the arguments we will make are the same as those taken by Schrödinger himself so you can see the lines of thinking a giant was making in his time. As a reminder, here is the time-dependent Schrödinger equation in 3-dimensions (for a non-relativistic particle) in all of its beauty:
Schrodingers Equation
The Schrodinger Equation