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tyneoh

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- Thread starter tyneoh
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tyneoh

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- #2

WannabeNewton

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Why do bound states have discrete energy spectra? It is just a consequence of the boundary conditions imposed on Schrodinger's equation. In classical EM if we have radiation bound to a cavity then Maxwell's equations together with these boundary conditions yeild a discrete spectrum of Fourier modes of the cavity radiation. With Schrodinger's equation the mathematical situation is almost entirely analogous (the PDEs differ in type) except now it applies to the spectrum of energy eigenstates of particles and as such also to the definite energies obtainable in this spectrum.

- #3

tyneoh

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What if the frequency of the photon decreases to the corresponding amount of the remainder energy? i.e. the frequency of the photon decreases after some of its energy is absorbed by the atom.

Why do bound states have discrete energy spectra? It is just a consequence of the boundary conditions imposed on Schrodinger's equation. In classical EM if we have radiation bound to a cavity then Maxwell's equations together with these boundary conditions yeild a discrete spectrum of Fourier modes of the cavity radiation. With Schrodinger's equation the mathematical situation is almost entirely analogous (the PDEs differ in type) except now it applies to the spectrum of energy eigenstates of particles and as such also to the definite energies obtainable in this spectrum.

- #4

WannabeNewton

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What if the frequency of the photon decreases to the corresponding amount of the remainder energy? i.e. the frequency of the photon decreases after some of its energy is absorbed by the atom.

The photon is absorbed by the electron. It doesn't exist anymore.

- #5

tyneoh

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Isn't the energy of a photon continuous, since its frequency can take on any value?The photon is absorbed by the electron. It doesn't exist anymore.

- #6

WannabeNewton

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Isn't the energy of a photon continuous, since its frequency can take on any value?

A single photon has a fixed frequency by definition.

- #7

tyneoh

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A single photon has a fixed frequency by definition.

OK so just to clarify, the quantum theory explains that radiation is carried by discrete packets of energy (photons) whose energy must also be discrete? Would that mean orange light from a sodium lamp cannot be changed in any way into other colours by altering the frequency of the "orange" photons?

- #8

Nugatory

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OK so just to clarify, the quantum theory explains that radiation is carried by discrete packets of energy (photons) whose energy must also be discrete?

Not quite. The quantum theory says that when radiation interacts with anything, it always delivers its energy in discrete packets; the theory is pretty much silent about what is "carrying" the radiation when it's just traveling through space. Thus, you cannot think of photons as particles traveling through space like little bullets (although this is the mental model that most people form when they first hear about them).

- #9

tyneoh

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Not quite. The quantum theory says that when radiation interacts with anything, it always delivers its energy in discrete packets; the theory is pretty much silent about what is "carrying" the radiation when it's just traveling through space. Thus, you cannot think of photons as particles traveling through space like little bullets (although this is the mental model that most people form when they first hear about them).

Then does the theory disallow the possibility of absorbing a portion the energy of an of an incoming say, violet photon and and render the photon into say, a green photon whose frequency corresponds to that of the remainder energy

- #10

Nugatory

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Then does the theory disallow the possibility of absorbing a portion the energy of an of an incoming say, violet photon and and render the photon into say, a green photon whose frequency corresponds to that of the remainder energy

Absorb a photon of given energy, then emit another of different energy? Sure, that works fine. Whether that's what happens or not depends on the particular interaction you're considering. For example, in the photoelectric effect the photon is absorbed delivering all of its energy to the electron, and any energy beyond what's needed to kick the electron free goes into the kinetic energy of the emitted electron. Other scattering processes will behave differently; for example Compton scattering will release a photon of lower energy than the one that came in.

- #11

tyneoh

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Absorb a photon of given energy, then emit another of different energy? Sure, that works fine. Whether that's what happens or not depends on the particular interaction you're considering. For example, in the photoelectric effect the photon is absorbed delivering all of its energy to the electron, and any energy beyond what's needed to kick the electron free goes into the kinetic energy of the emitted electron. Other scattering processes will behave differently; for example Compton scattering will release a photon of lower energy than the one that came in.

Right, how about an atom absorbing the excitation energy it needs from an incoming blue photon, and the photon leaves with the remainder of its original energy, except now that it has a lower frequency, say red?

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