A couple of questions about quantum mechanics.

[LiamSP]

Alright guys, I’ve been reading quite a bit about quantum mechanics lately (purely qualitative) and I have a couple of questions about it all, any help would be greatly Appreciated!


De Broglie Wavelength/schrondiger equation.

Ok, so I’ve heard the ‘Wave nature of patricles’ explained in a couple of ways.

1) The position and momentum of any microscopic particle can be described by it’s wave function, which can be calculated by solving the Schrödinger equation with regards to the particle your studying. This wave describes the probability of finding a particle in a particular area, this ‘wave function’ exhibits properties of a ‘traditional’ wave, this can explain the wave nature of particles.
For example, with regards to the double slit experiment for an electron/photon, the wave function is a super position of multiplepossibilities, 2 of these possibilities being the possibility of the particle passing through slit x and the possibility of the particle passing through slit Y. As these wave functions exhibit properties of normal waves, these 2 waves pass through slits x & y, and then interfere with each other. This then causes the formation of an interference pattern, so that some areas have a 0 chance of finding an electron, and some having a high chance, the particle in question then follows this distribution of probabilities two form the interference pattern we see.

2) Moving microscopic objects have an associated wavelength, Known as the de Broigle wavelength, this associated wavelength passes through both slits, interferes with itself thus causing an interference pattern
Are either of these correct ?

Secondley, with Regards to Alpha particle decay:

1) An alpha particle situated in the nucleus of an atom is confined to a very small area, due to the Heisenberg uncertainty principle the helium nucleus can have a large kinetic energy. This increase in energy means that the alpha particle has enough energy to escape the nucleus.

2) The wavefunction of the Alpha particle behaves like a normal wave, thus the wavefunction can exist out side the nucleus, suggesting that there is a small probability that the alpha particles can be outside the nucleus, thus decayed.

3) The actual answer is a combination of the 2 above suggestions.


Sorry for asking these questions but i think by clarifying these points it'll really help me make sense of somethings. Also, I apologise if this is in the wrong section, I'm new to this forum.

Any help much appreciated!

 

[azntoon]

Yes, both of these explanations are correct. The de Broglie wavelength is related to the wave-like properties of particles, which explains why two slits can produce an interference pattern when particles pass through them. As for alpha particle decay, it is a combination of the two explanations you have mentioned. The Heisenberg uncertainty principle states that the position and momentum of a particle cannot both be known with absolute certainty, so this allows for a small probability that the particle could be found outside the nucleus. Additionally, the wave-like properties of the particle allow for some of its wavefunction to extend outside the nucleus, thus increasing the likelihood of decay.