# Is Energy Truly Quantized in De Broglie's Equation?

• B
• _PJ_
In summary, De Broglie's equations of a quantised wave can be represented as E = h.nu, where h is Planck's constant and nu is frequency. This equation is further used to suggest that E is the "total energy" and is related to mc^2 through E = hf. For the relativistic form of these relationships, gamma is considered and can be found in the link provided. As for the non-zero ground state, it is not explicitly accounted for, and more information is needed to understand its relevance in this context.
_PJ_
Given De Broglie's equations of a quantised wave:

E = 2.Pi.hbar.c

Where:
E = Energy
Pi = PI (Ratio of circumference to radius)
hbar = Planck's constant (Reduced over 2.Pi)
c = celerity, causal displacement per time interval

In most texts this is summarised as:

E = h.nu

Where:
h = Planck's constant
nu = frequency

And E is suggested to be the "total energy"And then further used to imply that it is related by:

E= hf = mc^2

__________

Where is gamma? Why is there no consideration for Lorentz?
How is a non-zero ground state accounted for?
__________

_PJ_ said:
Where is gamma? Why is there no consideration for Lorentz?
Try this link for the relativistic form of these relationships: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/debrog2.html
How is a non-zero ground state accounted for?
I'm not sure I understand what you mean by "ground state" here. Can you give an example?

## 1. What is De Broglie's theory of wave-particle duality?

De Broglie's theory states that all particles, including electrons, have both wave-like and particle-like properties. This means that they can exhibit behaviors of both waves and particles, depending on the experimental setup.

## 2. How did De Broglie's theory impact the field of quantum mechanics?

De Broglie's theory provided a new understanding of the behavior of subatomic particles, which was not fully explained by classical physics. It helped to develop the concept of wavefunctions and the Schrödinger equation, which are key components of quantum mechanics.

## 3. What is the "rest mass" referred to in De Broglie's famous equation?

The "rest mass" in De Broglie's equation, E=mc², refers to the mass of a particle when it is at rest. It is a fundamental property of a particle and is a key factor in determining its behavior.

## 4. How did De Broglie's theory pave the way for the development of the electron microscope?

De Broglie's theory of wave-particle duality helped to explain the behavior of electrons in a vacuum, which was crucial in the development of the electron microscope. This microscope uses a beam of electrons instead of light to achieve much higher magnification and resolution.

## 5. What is the significance of De Broglie's theory in modern physics?

De Broglie's theory of wave-particle duality was a major breakthrough in our understanding of the behavior of subatomic particles. It has played a crucial role in the development of quantum mechanics, which is the foundation of modern physics. It has also led to numerous technological advancements, such as the development of particle accelerators and electron microscopes.

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