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Modern Physics
Found in: Page 224
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

Show that ψ(x)=A'eikx+B'e-ikx is equivalent to ψ(x)=Asinkx+Bcoskx, provided that A'=12(B-iA) B'=12(B+iA).

Hence, the proof for the equation is obtained.

See the step by step solution

Step by Step Solution

Step 1: Concept involved

According to the Euler’s formula in complex numbers, it can be written that:

eiφ=cosφ+isinφ (1)

Step 2: Given/known parameters

Consider the given function:


Consider the equations:

A'=12B-iA (2)

B'=12B+iA (3)

Step 3: Solution

Apply Euler’s formula from equation (1) and solve:


Rewrite the above equation as,

ψx=A'+B'coskx+A'-B'sinkx .. (4)

Now, by using equation (2) and (3) in equation (4) solve as:


Thus, you can say that: ψx=A'eikx+B'e-ikx is equivalent to

ψx=Bcoskx+Asinkx provided that A'=12B-iA and B'=12B+iA

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