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Since Schrödinger's equation doesn't show wavefunction decay or quantum decoherence, isn't it inaccurate to calculate the probability that a person or macroscopic object will quantum tunneling? I think the probability is zero if we include wavefunction collapse and quantum decoherence.

Nunes
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1 Answers1

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Decoherence still happens in the schrodinger model. All the different math frameworks for quantum i.e schrodinger, or hamiltonians, whichever you want, are exactly the same in terms of results from calculations. If you have a wavefunction that interacts with enviroment then you combine the wavefunction of the particle and that of the environment into a single wave function. Further if you meaured the particle to collapse it, what is really happening is you are combining your wavefunction with that of the particle.

Macroscopic objects have an expoentially small non 0 chance of tunneling. Schrodinger equations works perfectly well for basic quantum mechanics like this.

shai horowitz
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  • Aren't wavefunction collapse and quantum decoherence included in the Schrödinger equation? Does the Schrödinger equation contain quantum decoherence? – Nunes Jul 17 '22 at 15:04
  • If you look at the wave function for a ball , and then let that ball interact with the room, it seems like the wavefunction becomes non normalized. What really is going on is that your initial boundry conditions to your problem was set up wrong. You should look at the wavefunction for the "ball + room" this wave function is perfectly fit by the Schrodinger equation and predicts what will happen if you tried to factorize it to looking at only the ball. So yes it does. – shai horowitz Jul 17 '22 at 15:12
  • Exponetially small but NON 0. The interaction simply means you werent accounting for the complete wavefunction yet. After accounting for it you are still left with a perfectly fine wave function that can exhibit tunneling properties. – shai horowitz Jul 17 '22 at 15:45
  • I have answered your question and I'm now finished. Sorry you didnt get the answer you hoped to hear for whatever reason. maybe this may help you https://www.youtube.com/watch?v=iZKAtzK5WXM – shai horowitz Jul 17 '22 at 15:50
  • Can I ask you one more thing? Still, the quantum decoherence or wave function collapse interval is narrow, so the wave function continues to take on its initial shape, so isn't quantum events difficult in the macro world? Is there any probability that such a quantum event will occur even with a microscopic wavefunction? – Nunes Jul 17 '22 at 16:14
  • https://physics.stackexchange.com/a/243715/338089 – Nunes Jul 17 '22 at 17:30
  • ""The human body is composed out of ~10^23 particles (Avogadro's number). The wall will have orders of magnitude more in the proposed path through the wall. It is not possible to represent in a simple manner as in the image above the wave function of the system "human+wall" but a formalism exists, the density matrix, which allows for a many body representation. The density matrix formalism, gives that the probability of a complex object to tunnel through the wall barrier is effectively zero."" from the linked answer. effectively is not the same thing as 0. it means exponetially small. – shai horowitz Jul 17 '22 at 17:33
  • @nunes looking at your post history you've gotten this exact answer multiple times now. Is there a particular sticking point about the answer that makes you disagree with anyone else that I can help you on? – shai horowitz Jul 17 '22 at 21:19
  • I was asking because the quantum zeno effect doesn't allow the wavefunction to grow. – Nunes Jul 18 '22 at 03:48