Do protons and neutrons have a wavefunctions?

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Protons and neutrons do have wavefunctions, which include spatial, spin, and isospin components, although they are rarely explicitly written out in nuclear physics. Nuclear physicists often treat nucleons as being bound in a Coulomb potential, utilizing the shell model for nucleus description. In practice, nuclear wavefunctions are used abstractly to analyze nucleon states and interactions, such as singlet or triplet states and spin-orbit coupling. In atomic physics, the quantum properties of the nucleus can often be ignored, treating it as a classical collection of particles due to the significant mass difference between electrons and nucleons. Overall, every particle in the universe possesses a wavefunction.
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This might be a silly question, but do protons and neutrons have a wave function that they can be described by?
 
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Yes they do, but I don't think people ever worry about actually writing them out in nuclear physics. Protons have a wavefunction comprised of a spatial part and a spin part (and also an isospin part if you treat them as indistinguishable). For some reason nuclear physicists also assume that the neutrons and protons are bound in a more or less Coulomb potential, so that they can use the shell model to describe the nucleus. But when I took nuclear physics, we only used the nuclear wave functions at an abstract level to determine if nucleons were in a singlet or triplet state, spin-orbit coupling perturbations, etc.
 
In fact, every object in the universe has a wavefunction, I think.
 
Yes, every kind of particle has a wave function.

When we are doing atomic physics we can ignore the quantum properties of the nucleus and treat the nucleus as a stationary classical collection of particles, the reason for this is that the electron is over 1000 times less massive then the nucleons, and so it behaves more quantum mechanically.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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