# Is energy contained in matter wave equals hv like EM waves?

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In summary, the conversation discusses the use of h (Plank's constant) and v (frequency) to derive the TDSE. The issue arises when substituting k^2 in the equation E=h^2/8mpi^2 * k^2, where both the single derivative and double derivative of psi squared can be used, resulting in different equations. The person using the conversation's assumptions is also using the wave function psi = e^i(kx-wt). Further clarification on the starting assumptions is needed.

h is plank constant and v is frequency.
I was using this to derive the TDSE. But I ran into problem because to substitute k^2 in E=h^2/8mpi^2 * k^2, I can use single derivative of psi squared or double derivative, both of which tend to give the correct answer. So, is my assumption of energy wrong?

PS
I am using psi = e^i(kx-wt) as my wave function. Single derivative squared or double derivative both have k^2.
Substituting this gives two different equations.

I was using this to derive the TDSE.

Starting with what assumptions? Just saying "h is Planck's constant and v is frequency" isn't enough by itself.

Single derivative squared is not linear, whereas linearity is probably an assumption you want (though as PeterDonis said, you haven't stated what assumptions you want to start with fully).

## 1. What is the relationship between matter waves and energy?

The relationship between matter waves and energy is described by the equation E=hf, where E is energy, h is Planck's constant, and f is frequency. This equation is similar to the equation for electromagnetic waves, which is E=hc/λ, where c is the speed of light and λ is wavelength. Both equations show that the energy of a wave is directly proportional to its frequency.

## 2. How does the energy of a matter wave compare to the energy of an electromagnetic wave?

The energy of a matter wave is similar to the energy of an electromagnetic wave in that they both follow the same equation (E=hf). However, the difference lies in the values of h. For matter waves, h is Planck's constant, which is a very small value, whereas for electromagnetic waves, h is multiplied by the speed of light, making the energy of electromagnetic waves much larger than the energy of matter waves.

## 3. Does the energy of a matter wave depend on its amplitude?

No, the energy of a matter wave does not depend on its amplitude. Unlike electromagnetic waves, the energy of a matter wave is solely determined by its frequency. This is because matter waves, also known as de Broglie waves, are associated with particles, and the energy of a particle is determined by its frequency, not its amplitude.

## 4. Is there a limit to the energy of a matter wave?

Yes, there is a limit to the energy of a matter wave. According to the equation E=hf, the energy of a matter wave is directly proportional to its frequency. However, as the frequency of a matter wave increases, its wavelength decreases. This means that there is a point where the wavelength becomes so small that it cannot be detected, and at this point, the energy of the matter wave cannot be calculated.

## 5. How is the energy of a matter wave related to the mass of a particle?

The energy of a matter wave is related to the mass of a particle through the formula E=mc2. This formula, known as the mass-energy equivalence, was proposed by Albert Einstein and shows that there is a direct relationship between mass and energy. This means that matter waves, being associated with particles, also have a certain amount of energy based on their mass.