Potentials and de Broglie wavelength

In summary, the conversation discusses the Time Independent Schrodinger Equation and the use of the equation E=hc/λ for calculating the energy of a particle. The speaker inquires about using this equation for photons or electrons and the general de Broglie relation for any particle. There is also a question about the relevance of negative kinetic energy and the potential for the calculation. The conversation concludes with the possibility of using incorrect values and the need for clarification.
  • #1
Brewer
212
0

Homework Statement


work.jpg



Homework Equations


E=hc/λ?

and the Time Independent Schrodinger Equation.



The Attempt at a Solution



Now, would I be right in thinking for the first section that the energy for the E=hc/λ bit is just the energy of the particle given in the question (10eV).

Then for the other sections is the relevant energy just 10eV minus the potential?

As the last section will give a negative KE of the particle does that mean that it doesn't have a de Broglie wavelength? Its just a negatively decaying exponential (i.e. tending to 0)?


Does that sound like I'm on the right lines?
 
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  • #2
Anyone have any hints about this one? The way that I described it above is the way that I attempted it, and after using the wrong values from my data sheet (first I used k(why I picked this I don't know - maybe I just can't read!) and then [tex]\hbar[/tex] before reading the sheet properly for the value of h!) I think I have values that give decent answers.
 
  • #3
It sounds fine to me. Decaying exponential in the last region, yes. Is there still a question?
 
  • #4
Brewer said:

Homework Statement


work.jpg



Homework Equations


E=hc/λ?
Are we talking about photons or electrons? What is the general de Broglie relation for any particle?
 

FAQ: Potentials and de Broglie wavelength

1. What is a potential in the context of physics?

A potential in physics refers to the amount of energy that an object or system possesses in relation to its position or configuration. It is often represented by the symbol V and can be either a scalar quantity, such as gravitational potential, or a vector quantity, such as electric potential.

2. What is the significance of potentials in quantum mechanics?

In quantum mechanics, potentials play a crucial role in determining the behavior and properties of particles. They can affect the probability of a particle's position and momentum, as well as the energy levels of a system. Potentials also help explain phenomena such as quantum tunneling and the wave-like nature of particles.

3. How is the de Broglie wavelength related to potentials?

The de Broglie wavelength is a concept in quantum mechanics that relates the momentum of a particle to its wavelength. It is directly affected by the potential that the particle is in, as the potential can either increase or decrease the particle's momentum and therefore its wavelength. In a potential-free region, the de Broglie wavelength is constant.

4. Can potentials and de Broglie wavelength be observed in experiments?

Yes, both potentials and de Broglie wavelength can be observed in various experiments. For example, the double-slit experiment demonstrates the wave-like behavior of particles, including their de Broglie wavelength. In addition, experiments with charged particles in electric and magnetic fields can demonstrate the effects of potentials on particle behavior.

5. How do potentials and de Broglie wavelength relate to the uncertainty principle?

The uncertainty principle, a fundamental principle in quantum mechanics, states that it is impossible to simultaneously know the exact position and momentum of a particle. This is directly related to potentials and de Broglie wavelength, as the potential of a particle affects its momentum, and the de Broglie wavelength is inversely proportional to the particle's momentum. Therefore, the uncertainty principle applies to both potentials and de Broglie wavelength in terms of their effect on the behavior of particles.

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