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Physics, 27.07.2019 02:10 87haymaker

The fundamental equation of quantum mechanics is the schrödinger equation. for many systems, we'll find solutions to this equation involve oscillatory functions, such as sine and cosine. euler's formula provides a convenient way of representing these functions using complex numbers i0 a. using euler's formula, show that: ae ae-ikr bear-be- ) ) a cos (kx) and b sin k = = 2i where a, b, and k are arbitrary constants. -ikx show that a-+beer can be rearranged into the sumacos(k) + βsin(kr) where α and β are arbitrary constants. how do α and β relate to a and b? b. c. show that ae +be can also be written as: csin(kr + φ) where c and φ are constants. derive expressions that relate c and φ to a and b. hint: consider rewriting the sine function above using the result of part (a). d. use euler's formula to find the values of m that satisfy the equation exp(2rim) 1. these values describe the solution to the schrödinger equation for a mass moving in a circle! if you need a refresher on how to do this, take a look at mathchapter a from mcquarrie & simon or section 1-5 of applied mathematics for physical chemistry by james r. barrante.

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