Probability distribution of the momentum value p

In summary, the conversation discusses the difficulty of determining the probability distribution of the momentum value in the ground state of the hydrogen atom and suggests using a one dimensional square potential well to model it. One person suggests using the hydrogen atom's atomic diameter as the well width, while another suggests using Fourier transform to get the exact result.
  • #1
NEWO
95
0
gosh this work is causing me some grief,

if some one can highlight a few tips i would be greatfull

q) determine the probability distribution of the momentum value p in the ground state of the hydrogen atom?

i know what the groundstate of the of the hydrogen atom is but i don't know how to apply it to this

thanks for any help

newo
 
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  • #2
You should be able to model the hydrogen atom using the one dimensional square potential well with sides x=0, x=L. Use hydrogen's atomic diameter as the well width.
 
  • #3
Why not just Fourier transform the ground state wavefunction and get the exact result?
 

1. What is the probability distribution of the momentum value p?

The probability distribution of the momentum value p is the likelihood of obtaining a certain momentum value in a given system. It describes the relative frequency of different values of momentum in a group of particles or objects.

2. How is the probability distribution of the momentum value p calculated?

The probability distribution of the momentum value p is calculated using the momentum probability density function, which takes into account the mass, velocity, and position of each individual particle or object in the system. This function is then integrated over all possible momentum values to determine the overall probability distribution.

3. What factors can affect the probability distribution of the momentum value p?

The probability distribution of the momentum value p can be affected by the temperature, pressure, and density of the system, as well as any external forces acting on the particles or objects. It can also be influenced by quantum effects in the case of subatomic particles.

4. How does the probability distribution of the momentum value p relate to the uncertainty principle?

The uncertainty principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. The probability distribution of the momentum value p reflects this uncertainty by showing a spread of possible momentum values rather than a single definite value.

5. Can the probability distribution of the momentum value p change over time?

Yes, the probability distribution of the momentum value p can change over time as the system evolves. This can occur due to interactions between particles, changes in external forces, or changes in the system's temperature, pressure, or density. The distribution may also fluctuate due to quantum effects.

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