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What is the amplitude of a single photon's wave? Yes, it's well taught that wavelength is related to frequency. Higher frequency is higher energy energy and l

What is the amplitude of a single photon's wave? Yes, it's well taught that wavelength is related to frequency. Higher frequency is higher energy energy and lower frequency is lower energy, but it's the frequency of what? Unlike ocean waves, photons do not have a spacial amplitude. A photon does however have a spacial wavelength. This distinction between photonic wavelength and amplitude I've never heard explicitly addressed. My understanding is that a photon's amplitude is the likelihood of interaction at a specific point in space. High amplitude is likely interaction, low amplitude is low likelihood of interaction. This means at a photon's peaks/crests it has high interaction and at its troughs the photon has low interaction likelihood. These likelihoods are repeated every wavelength, a length measurable in physical space. This is some of the reason why an antenna for a given frequency range needs to be a specific size. Too small and there's a good chance of missing a signal. A proper sized antenna, related to wavelength, guarantees high interaction somewhere along the length of the antenna. When speaking of many photons, amplitude (like AM radio) is simply flux, how many photons at a particular frequency exist during a given unit of time. That's not related to the amplitude of a single photon and not what I'm talking about here.

noobermin 6y ago
Quanta are specifically the quantization of the EM field, so if you will, a single photon at least theoretically is the smallest amplitude of an EM wave you can have. You can see this mostly by noting the expectation of the number operator gives essentially the radiant intensity.
pdonis 6y ago
> My understanding is that a photon's amplitude is the likelihood of interaction at a specific point in space. Not really, because there isn't really a well-defined wave function for a photon in the position representation (which is the one that has the interpretation "the likelihood of detection at a specific point in space"). > When speaking of many photons, amplitude (like AM radio) is simply flux, how many photons at a particular frequency exist during a given unit of time. There isn't a well-defined answer to this question, because a state like this (which is a coherent state) is not an eigenstate of the photon number operator. (Also, energy flux is really amplitude squared.) A good, if somewhat lengthy, discussion of the "photon" concept can be found here: http://math.ucr.edu/home/baez/photon/schmoton.htm http://math.ucr.edu/home/baez/photon/schmoton.htm
krastanov 6y ago
We have to first specify what you mean by amplitude of single photon. Are you asking what would be the E-field observed from a single photon? That is well defined, however it depends on what photon you are talking about. Is it a photon confined to a cavity made of perfect mirrors? Is it a photon with well defined "position" and poorly defined "frequency"? In all these cases you can answer "what is the E field for a single photon", and you need mostly classical electromagnetism to answer this. Are you asking about the probability amplitude of the state? This can kinda be answered in the confines of Quantum Mechanics by talking about Klein-Gordon's equation, but truly, it is a mess and not a particularly practical approach. To get useful results you probably need to switch to a more general formalism called Quantum Field Theory, and in that formalism the pop-sci handwavy talk about wave-functions breaks a bit, but it also has a well defined answer.
knzhou 6y ago
> What is the amplitude of a single photon's wave? That doesn't have a well-defined answer, unfortunately. Suppose the electromagnetic field contains a single photon. Its electric field then necessarily exists in a superposition of values, so it doesn't have a well-defined amplitude. It also doesn't have a definite "typical" amplitude either -- that depends on how spread out the photon is, and its frequency. As a rough estimate, a photon of frequency omega has energy hbar omega, so if it's spread out over a volume V, then matching energy densities gives E^2 V ~ hbar omega, so you expect the rms value of E to be of order hbar omega / V.
nabla9 6y ago
> My understanding is that a photon's amplitude is the likelihood of interaction at a specific point in space. High amplitude is likely interaction, No. Electromagnetic wave and quantum wave function are two different waves.
caf 6y ago
Ordinary sound waves don't have an amplitude defined by a spatial displacement either - they're pressure waves, where the amplitude is a measure of the change in a scalar that is defined for each position in the volume of interest (the pressure/density). Similarly for an EM wave the amplitude is the change in a value that is defined for each position in the space of interest - the electromagnetic field strength, although this value is a vector not a scalar. (The EM field is always perpendicular to the direction of propagation of the wave, so for any propagation direction there's only one degree of freedom left which is the "polarisation angle").

noobermin 6y ago

Quanta are specifically the quantization of the EM field, so if you will, a single photon at least theoretically is the smallest amplitude of an EM wave you can have. You can see this mostly by noting the expectation of the number operator gives essentially the radiant intensity.

pdonis 6y ago

> My understanding is that a photon's amplitude is the likelihood of interaction at a specific point in space. Not really, because there isn't really a well-defined wave function for a photon in the position representation (which is the one that has the interpretation "the likelihood of detection at a specific point in space"). > When speaking of many photons, amplitude (like AM radio) is simply flux, how many photons at a particular frequency exist during a given unit of time. There isn't a well-defined answer to this question, because a state like this (which is a coherent state) is not an eigenstate of the photon number operator. (Also, energy flux is really amplitude squared.) A good, if somewhat lengthy, discussion of the "photon" concept can be found here: http://math.ucr.edu/home/baez/photon/schmoton.htm http://math.ucr.edu/home/baez/photon/schmoton.htm

krastanov 6y ago

We have to first specify what you mean by amplitude of single photon. Are you asking what would be the E-field observed from a single photon? That is well defined, however it depends on what photon you are talking about. Is it a photon confined to a cavity made of perfect mirrors? Is it a photon with well defined "position" and poorly defined "frequency"? In all these cases you can answer "what is the E field for a single photon", and you need mostly classical electromagnetism to answer this. Are you asking about the probability amplitude of the state? This can kinda be answered in the confines of Quantum Mechanics by talking about Klein-Gordon's equation, but truly, it is a mess and not a particularly practical approach. To get useful results you probably need to switch to a more general formalism called Quantum Field Theory, and in that formalism the pop-sci handwavy talk about wave-functions breaks a bit, but it also has a well defined answer.

knzhou 6y ago

> What is the amplitude of a single photon's wave? That doesn't have a well-defined answer, unfortunately. Suppose the electromagnetic field contains a single photon. Its electric field then necessarily exists in a superposition of values, so it doesn't have a well-defined amplitude. It also doesn't have a definite "typical" amplitude either -- that depends on how spread out the photon is, and its frequency. As a rough estimate, a photon of frequency omega has energy hbar omega, so if it's spread out over a volume V, then matching energy densities gives E^2 V ~ hbar omega, so you expect the rms value of E to be of order hbar omega / V.

nabla9 6y ago

> My understanding is that a photon's amplitude is the likelihood of interaction at a specific point in space. High amplitude is likely interaction, No. Electromagnetic wave and quantum wave function are two different waves.

caf 6y ago

Ordinary sound waves don't have an amplitude defined by a spatial displacement either - they're pressure waves, where the amplitude is a measure of the change in a scalar that is defined for each position in the volume of interest (the pressure/density). Similarly for an EM wave the amplitude is the change in a value that is defined for each position in the space of interest - the electromagnetic field strength, although this value is a vector not a scalar. (The EM field is always perpendicular to the direction of propagation of the wave, so for any propagation direction there's only one degree of freedom left which is the "polarisation angle").