Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966)ĭ. Gauthier, This derivation of the classical wave equation follows that given by Gauthier. The last section in this chapter discusses what conditions must be applied to solutions of Schrödinger’s equation and their interpretation. The interpretation of this function is unusual in that it deals with probabilities. The solution of Schrödinger’s equation for any particular sitaution often leads to multiple possible wavefunctions and corresponding energies. Associated with any wavefunction is also corresponding energy. Solutions to Schrödinger’s equation take the form of a mathematical function usually written as \(\psi (x)\) and which is known as a “wavfunction”. In 1927 he published his uncertainty principle. For that discovery, he was awarded the Nobel Prize for Physics for 1932. There are actually two versions of Schrödinger’s equation, one time-dependent and one time-independent while the focus in this book is on the latter, both are developed in this chapter. Werner Heisenberg (born December 5, 1901, Wrzburg, Germanydied February 1, 1976, Munich, West Germany) German physicist and philosopher who discovered (1925) a way to formulate quantum mechanics in terms of matrices. Like Newton’s laws of motion, there is no rigorous derivation or proof of Schrödinger’s equation, but a plausibility argument based on the classical wave equation and energy concepts is presented. Schrödinger’s equation is a type of “wave” equation, so this chapter opens with a description of the “classical” wave equation, that which would be used to describe a traveling wave propagating along a string such as one encounters in elementary physics. This chapter develops Schrödinger’s equation, the fundamental law of quantum physics.
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