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It seems like the thing you are missing is a very basic ingredient of quantum mechanics -- the Born rule. When we make a measurement of some observable $A$, we will find that $A$ takes values in the eigenvalues $a_i$ of the corresponding operator $A$. The Born rule tells us that, for a system initially in the state $\left|\psi\right>$, the probability of ...

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I would forget about the movement of the wall. The potential is the infinite square well of width $2L$ (potential is $\infty$ aside from the region $0 < x < 2L$, where it is $0$), and the wavefunction is $$\Psi\left(x,t\right) = \sum_{n=1}^\infty c_n \psi_n\left(x\right) \exp\left(-\frac{iE_n t}{\hbar}\right),$$ where $\psi_n\left(x\right) = ... 4 Another way to look at spin, complementary to the other ways, which I find helpful is look at an abstract generalisation of the concept of angular momentum and forget about things like classical tops. This generalisation begins in something called Noether's Theorem which you probably haven't met yet. You need some background but the idea is essentially ... 1 Quantum Spin of a particle just represents another degree of freedom (e.g$+/- 1/2\$ for electrons) and due to its representation as an "angular momentum operator", it is refered to as "spin". However it is not an analog (or actual revolution of a particle around its own axis). At least not in a classical sense. In summary it represents another degree of ...

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...it makes no sense to calculate any property of the particle with the "initial" wave-function, since this is simply the incorrect wave-function for the new well? The wavefunction can't be "incorrect for the well". Your wavefunction is just an initial condition for time-dependent Schrödinger equation. Here's how it would evolve if you solve the ...

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Electrons never follow "particle principles", by which you seem to mean the physics of classical point particles. It's only in certain cases that a classical approximation is sufficient for human purposes, i.e. when we don't care about the uncertainty relations that govern quantum mechanical objects. In general it's better to think about elementary ...

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Spin is not defined as the spin of electron around its own axis. Spin is the intrinsic angular momentum of the electron - intrinsic meaning it does not arise from the electron's motion, but is a property of electron itself. The electron in the atom "can" be described as a particle if you are using the Bohr model of the atom. Quantum mechanical picture of ...

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