In quantum mechanics we studied that everything has a wave function associated with it.My question is can we write down the wave functions of things. Then how we can write down the wave functions of the things like animals, human eye, motion of snake etc.
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2$\begingroup$ Yes, animals (and humans etc.) may be described just like any other composite objects built from elementary particles. $\endgroup$– Luboš MotlCommented Jun 4, 2016 at 15:18
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1$\begingroup$ It means we consider their wave function in terms of the particles they are made of,not as a whole? $\endgroup$– Memoona MehmoodCommented Jun 4, 2016 at 15:26
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$\begingroup$ Thanks very much for your vote Memoona, but there are lots of people on this site who know far more than I do about Q.M, so there is no need to rush if you get a more elaborate or refined answer later. $\endgroup$– user108787Commented Jun 4, 2016 at 15:43
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2 Answers
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There are 37.2 trillion cells in a typical human body, (probably a good few more in mine ;), then in each cell there are 20 trillion atoms, then you have to obtain the wave function for each of the electrons.......
Actually, it may well be that you cannot describe a wavefunction for a macroscopic object, like a human body. In the study of quantum mechanics, we are usually presented with the exercise of writing a wave equation for a single microscopic particle, an electron, proton and so on.
But a macroscopic object is "joined" to it's surroundings by entanglement, rather than the single electron wavefunctions we are used to deal with, which does not need to take account of this.
If two (or more) systems are entangled, such as the parts of our body and their surroundings, as in this case, then we cannot describe the wave function directly as a product of separate wavefunctions, as I implied incorrectly in my first line.
However, by the use of Reduced Density Matrices, as pointed out by Mitchell Porter below, we can describe entangled states. With the number of wave functions involved, this would theorically possible, but in practice, not a feasible option.
Incidentally, this may be one reason why the STAR TREK, "beam me aboard" transporter system may be rather difficult to achieve, but that is probably covered elsewhere on this site.
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$\begingroup$ @count_to_10 If an object is entangled with its environment, you can describe its state with en.wikipedia.org/wiki/… $\endgroup$ Commented Jun 4, 2016 at 20:59
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$\begingroup$ How do we determine where entanglement begins and ends? Like if I drive a car am I entangled with it or just sitting in it? Am I entangled with the wind, the sky, the Universe? Some on more levels than others? $\endgroup$– p1l0tCommented Dec 8, 2021 at 19:09
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My answer will be very non-technical, but hopefully will convey some basic ideas about what the quantum state (or wavefunction) is about.
One intuitive way to picture the nature of the quantum state of a system is to see it as the interference (hence the "wave" idea) of every different changes it could possibly undergo while it is not being messed with.
In other words, when a system is not observed, its dynamics takes into account absolutely all the behaviors it could have and somehow mixes them together in constructive and destructive ways (this is known as the "path integral").
There are two aspects here that make it impossible in practice to formulate the wavefunction of a living being:
First, if the system is not isolated one must take into account all interactions it has with its environment (which is made of other systems themselves subject to the same description). Living beings are obviously not isolated, they are very open systems continuously exchanging matter and energy with their environment.
Second, for anything else than simple systems there is no way to build the interference of all possible behaviors, because they can be very complex and there is an infinity of them.
answered Jun 4, 2016 at 16:15