SHORT ANSWER SECTION (3 pts each) help derive the TOSE. Define each symbal in th
ID: 3280059 • Letter: S
Question
SHORT ANSWER SECTION (3 pts each) help derive the TOSE. Define each symbal in the simgle equation 2. h/p was already known when de Brode made his hypothes what then, precie .washishmthen? 3. Write the mathematical form of a free partide eigenfunction. What are the allowed values of 4. Write the mathematical form of a PIB eigenfunction. What are allowed values of k 5. If k/m = 9, what is the value of the zero part energy for a SHO? 6. Why are eigenfunctions also called stationary states? . Why are eigenfunctions also called eigenvectors? . What frequency of beats results from a superposition of the first excited and 3't excited statesExplanation / Answer
Problem 2)
The De Broglie hypothesis proposes that all matter exhibits wave-like properties and relates the observed wavelength of matter to its momentum. After Albert Einstein's photon theorybecame accepted, the question became whether this was true only for light or whether material objects also exhibited wave-like behavior. Here is how the De Broglie hypothesis was developed.
Considering Einstein's relationship of wavelength lambda to momentum p, de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:
lambda = h / p
This wavelength is called the de Broglie wavelength. The reason he chose the momentum equation over the energy equation is that it was unclear, with matter, whether E should be total energy, kinetic energy, or total relativistic energy. For photons, they are all the same, but not so for matter.
Assuming the momentum relationship, however, allowed the derivation of a similar de Broglie relationship for frequency f using the kinetic energy Ek:
f = Ek / h
De Broglie's relationships are sometimes expressed in terms of Dirac's constant, h-bar = h / (2pi), and the angular frequency w and wavenumber k:
p = h-bar x k
Ek = h-bar x w
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