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Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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Can we measure $x$ and $p_x$ simultaneously by measuring $p_y$ and $y$ as well?

In this case, we can consider the state $|\psi\rangle_{xy}$ in the $xy$ plane to be a tensor product of two one-dimensional states, $|\psi\rangle_x$ and $|\psi\rangle_y$. These states are independent: …
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What is the physical intuition for Bloch Sphere?

Imagine we're considering the spin of an electron. We denote the two possible measurement outcomes in the $z$ direction $|0\rangle =\begin{pmatrix}1\\ 0\end{pmatrix} = $ spin up and $|1\rangle=\begin{ …