Showing Superposition Principle with Time-Dependent Schrödinger Equation

AI Thread Summary
To demonstrate that the combination of two solutions of the time-dependent Schrödinger equation is also a solution, one must substitute the linear combination c1*psi1 + c2*psi2 into the equation. This process involves verifying that the resulting expression satisfies the equation for arbitrary constants c1 and c2. The superposition principle is key to this proof, as it allows for the addition of solutions. Many resources simply state this as a fact without detailed explanation. Ultimately, the solution requires direct substitution and verification within the framework of the Schrödinger equation.
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Homework Statement


Show that, if psi1 and psi2 are both solutions of the time-dependent Schr¨odinger
equation, so is c(subscipt1) psi1 + c(subscript2) psi2 (where c1 and c2 are arbitrary constants).


Homework Equations





The Attempt at a Solution


every source I've consulted so far just states it as a fact. i know its somthing to do with the superposition principle but how do i literally show what they ask? its only a 2 markk que
thanks in advance
 
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Just plug that combination into the Schrodinger equation and show it satisfies the equation.
 

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