Bohm-WKB2011

Bohm-WKB2011 - Physical Chemistry Course Number: C362 14...

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Unformatted text preview: Physical Chemistry Course Number: C362 14 Extra-credit Homework: Classical mechanics as a special case of quantum mechanics This homework will help you see how the classical Newtonian equations arise as a special case of the time-dependent Schrodinger Equation. You will also see how alternate interpretations are possible for the wavefunction. This homework will give you a fleeting overview of correspondence between classical and quantum mechanics. This derivation was first performed by Madelung and de Broglie in 1926 and later by David Bohm in 1952. In fact Bohm generalized this to something called the Bohms interpretation of quantum mechanics a very classical-like interpre- tation. In modern parlons, Bohms interpretation is also known as the hidden- variable interpretation of quantum mechanics. Dont worry, I will work you through the homework: 1. Go ahead and substitute ( x, t ) = A exp ( S / h ) in the time-dependent Schrodinger Equation. 2. Does = A exp ( S / h ) make sense? The wavefunction can be complex. And certainly any complex number can be written in this form. (Please see the complex numbers handout) Provide a brief explanation as to why any complex number can be written in this form. (Hint: Say z = x + y is a complex number. Can you write z = a exp { } ? What would the values of a and be if this were to hold true?)be if this were to hold true?...
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This note was uploaded on 01/17/2012 for the course C 362 taught by Professor Amarflood during the Winter '11 term at Indiana.

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Bohm-WKB2011 - Physical Chemistry Course Number: C362 14...

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