# Wave function with a certain wavelength

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In summary, the conversation discusses the wave function and its implications for photons. It is noted that photons do not follow the Schrödinger equation and that their uncertainty in position can affect their wavelength. It is also mentioned that the uncertainty in wavelength can be small even with a larger uncertainty in position due to the small value of Planck's constant.

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I have a number of questions about the wave function -
1. Do photons have wave functions like the one in Schrodinger equation?
2. If they do, when you send out a wave function with a certain wavelength, then because you know the momentum with no uncertainty the uncertainty of the position becomes infinite and you don't know where the photon is. What happens then? For example if you send out that wave to experiment the photoelectric effect, when the light(photon) hits the particle then the particle 'knows' where the photon is and therefore its uncertainty in the position becomes very small, and as a consequence the uncertainty in the momentum becomes very large; does this mean that the light will suddenly have various wavelengths?

My guess for question 2 is that you can't send out a light of definite wavelength.

Any wave packet will contain several wavelengths unless it is infinitely extended. This is true for all waves. However, note that ##\hbar## is very small. You can have a wave with a very small uncertainty in wavelength even if your uncertainty in position is of the order of magnitude you would expect from the photoelectric effect.

Also, photons definitely do not follow the Schrödinger equation. The Schrödinger equation describes a non-relativistic massive particle, which the photon most certainly is not. It is about as far away from it as you can get.

## 1. What is a wave function with a certain wavelength?

A wave function with a certain wavelength refers to the mathematical representation of a wave, which describes the amplitude and phase of the wave at each point in space and time. The wavelength is the distance between two corresponding points on the wave, such as two peaks or two troughs.

## 2. How is wavelength related to energy?

According to the wave-particle duality of quantum mechanics, particles can also behave as waves. The wavelength of a particle corresponds to its energy through the de Broglie relation, where shorter wavelengths correspond to higher energies. This relationship allows us to study the energy levels and properties of particles through their wave functions.

## 3. Can a wave function have multiple wavelengths?

Yes, a wave function can have multiple wavelengths if it is a superposition of multiple waves with different wavelengths. This is known as a complex wave function and is commonly used in quantum mechanics to describe complex systems.

## 4. What is the significance of the wavelength in wave functions?

The wavelength of a wave function is important as it determines the properties and behavior of the wave. For example, the wavelength of an electromagnetic wave determines its color and energy, while the wavelength of a particle wave function determines its momentum and position uncertainty.

## 5. How is wavelength related to the uncertainty principle?

The uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a particle. This is related to the wavelength of the particle's wave function, as a smaller wavelength corresponds to a more well-defined momentum and a larger wavelength corresponds to a more uncertain momentum. Therefore, the uncertainty principle puts a limit on how precisely we can know the wavelength of a particle's wave function.