Schrodinger Equation: Kinetic Energy Impact?

In summary, the Schrodinger equation includes the Hamiltonian, which is comprised of the Kinetic energy operator. In this equation, Schrodinger converted momentum to the unit imaginary number, the reduced Planck constant, and the Delta operator. This means that the Kinetic energy will be the same for all quantum level particles, regardless of their characteristics. However, this may seem counterintuitive as Kinetic energy is a form of energy and should affect the evolution of the state. The relation between the classical Hamilton function and the Hamilton operator is used in both classical and quantum mechanics, with the kinetic energy expressed via momentum. In quantum mechanics, momentum is replaced with an operator acting on quantum states or wave functions.
  • #1
HarryDaniels
43
0
I am sure you are all aware of the Schrodinger equation.

The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrodinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator.

My question is that this means that the Kinetic energy will be the same regardless of the characteristics of the quantum level particle. This does not make sense, surely the kinetic energy will affect the evolution of the state, due to the fact that it is energy.

Thanks to whoever clears this up for me.

-H
 
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  • #2
HarryDaniels said:
I am sure you are all aware of the Schrodinger equation.

The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrodinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator.

My question is that this means that the Kinetic energy will be the same regardless of the characteristics of the quantum level particle. This does not make sense, surely the kinetic energy will affect the evolution of the state, due to the fact that it is energy.

Thanks to whoever clears this up for me.

-H

Can you clarify your question?

The Hamiltonian is E = Ke + V where Ke is the kinetic component and V is the potential component.

Kinetic energy is related to the angular momentum and the momentum at any given point is the curvature of the particle at that point which changes with quantum state.
 
  • #3
I am not sure if you are aware of the relation between the classical Hamilton function and the Hamilton operator.

In both classical and quantum mechanics we can write

[tex]H = E_\text{kin} + E_\text{pot}[/tex]

The kinetic energy is expressed via the momentum as

[tex]E_\text{kin} = \frac{p^2}{2m}[/tex]

In quantum mechanics you replace

[tex]p \to \hat{p} = -i\partial_x[/tex]

and therefore you convert the Hamilton function in an operator acting on quantum states or wave functions.
 

1. What is the Schrodinger Equation?

The Schrodinger Equation is a mathematical equation that describes how the quantum state of a physical system changes over time. It is a fundamental equation in quantum mechanics and is used to calculate the probability of finding a particle in a certain state at a certain time.

2. How does the Schrodinger Equation impact kinetic energy?

The Schrodinger Equation describes the total energy of a particle, which includes both its potential energy and kinetic energy. It allows us to calculate the kinetic energy of a particle in a quantum system, which is important in understanding the behavior of particles at the atomic and subatomic level.

3. What is the relationship between the Schrodinger Equation and the Heisenberg uncertainty principle?

The Schrodinger Equation is used to calculate the probability of finding a particle in a certain state, while the Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. The Schrodinger Equation helps us understand and quantify this uncertainty in quantum systems.

4. How does the Schrodinger Equation impact our understanding of the physical world?

The Schrodinger Equation is a cornerstone of quantum mechanics, which is the branch of physics that studies the behavior of particles at the atomic and subatomic level. It allows us to make predictions and understand the behavior of particles that cannot be explained by classical physics, and has revolutionized our understanding of the physical world.

5. What are some real-world applications of the Schrodinger Equation?

The Schrodinger Equation has numerous applications in modern technology, such as in the development of semiconductors for electronic devices, the design of new materials for use in solar cells and batteries, and in the development of quantum computing. It is also used in fields such as chemistry, biology, and materials science to understand the behavior of molecules and materials at the atomic level.

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