- #1

Feynmanfan

- 129

- 0

I am asked to calculate the uncertainty of the electron's momentum. I don't really know where to start from.

Thanks for your advice

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Feynmanfan
- Start date

In summary, the infinite potential well is a theoretical model used in quantum mechanics to describe a confined particle with infinitely high potential barriers. It works by restricting the particle to specific energy levels and using a standing wave pattern to describe its wave function. This model has various applications in quantum mechanics, including explaining the behavior of particles in atoms and solid materials. However, it has limitations such as assuming a perfectly confined space and not accounting for external forces. Additionally, it is related to the uncertainty principle, as the precise position of the particle in the infinite potential well leads to a range of possible momenta due to its wave nature.

- #1

Feynmanfan

- 129

- 0

I am asked to calculate the uncertainty of the electron's momentum. I don't really know where to start from.

Thanks for your advice

Physics news on Phys.org

- #2

- 13,358

- 3,455

How about the definition of the uncertainty...?

Daniel.

Daniel.

- #3

thepatientmental

- 1,016

- 0

To calculate the uncertainty of the electron's momentum, you can use the uncertainty principle, which states that the product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 2π. In this case, since the electron is in the lowest energy level (n=1) of an infinite potential well, the wave function can be described by a sine function with a wavelength equal to the width of the well. This means that the position of the electron is well defined within the well, but its momentum is uncertain.

To calculate the uncertainty in momentum, you can use the formula Δp = h/λ, where Δp is the uncertainty in momentum, h is Planck's constant, and λ is the wavelength of the electron's wave function. In this case, since the electron's wave function corresponds to the lowest energy level (n=1), the wavelength can be determined from the de Broglie relation, which states that the wavelength of a particle is equal to h/p, where p is the momentum of the particle. Since the electron is in the lowest energy level, its momentum can be determined from the energy eigenvalue of the system, which is given by E = p^2/2m, where m is the mass of the electron. Putting these equations together, we get:

Δp = h/(h/p) = p

Therefore, the uncertainty in momentum is equal to the momentum itself. This means that the uncertainty in momentum is not a fixed value, but rather depends on the value of the electron's momentum. In general, the uncertainty in momentum will be smaller for particles with larger momentum and vice versa.

In summary, the uncertainty principle tells us that the product of the uncertainties in position and momentum is always greater than or equal to Planck's constant divided by 2π. In the case of an electron in an infinite potential well in the lowest energy level, the uncertainty in momentum is equal to the momentum itself, which can be determined from the energy eigenvalue of the system. I hope this helps guide you in your calculations.

An infinite potential well is a theoretical model used in quantum mechanics to describe the behavior of a particle that is confined within a finite space with infinitely high potential barriers on all sides. It is often used to demonstrate the principles of quantum confinement and particle wave behavior.

In the infinite potential well model, the particle is restricted to a certain region and has a total energy that is equal to the energy of its bound states. This means that the particle can only exist in specific discrete energy levels, and its wave function is described by a standing wave pattern.

The infinite potential well model has various applications in quantum mechanics, including explaining the behavior of electrons in atoms, the properties of solid materials, and the behavior of particles in a confined space such as a quantum dot. It is also used to understand the behavior of photons in optical systems.

Although the infinite potential well model is a useful theoretical tool, it has its limitations. It assumes a perfectly confined space with infinitely high potential barriers, which is not possible in reality. It also does not take into account the effects of external forces such as gravity and electromagnetic fields.

The infinite potential well model is related to the uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. In the infinite potential well, the particle's position is known precisely, but its momentum can only be described by a range of values due to the wave nature of the particle.

- Replies
- 1

- Views
- 799

- Replies
- 18

- Views
- 2K

- Replies
- 27

- Views
- 2K

- Replies
- 2

- Views
- 779

- Replies
- 3

- Views
- 1K

- Replies
- 31

- Views
- 2K

- Replies
- 22

- Views
- 1K

- Replies
- 15

- Views
- 803

- Replies
- 8

- Views
- 3K

- Replies
- 1

- Views
- 1K

Share: