# Tagged Questions

For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

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### Qubits and vector projections

In $\Bbb C^2$, how many real unit vectors are there whose projection onto $|1\rangle$ has length $\sqrt{3}/2$? I would think zero as $\bigl(\frac{\sqrt{3}}{2}\bigr)^2 + x^2 = 1$, therefore there are ...
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### Entanglement and linear algebra

How do you represent entanglement of two particles in quantum mechanics using linear algebra? How does measure of one particle affecting the state of other quantum mechanically captured linear ...
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### eigenenergies when Hamiltonian is $\hat{H}^2$ − $\hat{H}$

If the eigenenergies of the Hamiltonian $\hat{H}$ are $E_n$ and the eigenfunctions are $\psi_n(r)$ , what are the eigenvalues and eigenfunctions of the operator $\hat{H}^2$ − $\hat{H}$ ? Attempted ...
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### Distinct eigenvalues of matrix

While studing Quantum Physics I've came to the conclusion that it would be useful to find an equivalent (or at least a sufficient) condition for a matrix (over $\mathbb{C}$) to have distinct ...
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### Example of using the Hadamard's matrix to determine the superposition

I've came across those notes for Quantum computation from John Watrous. I am having troubles understanding the last example. We have those two vectors, or if I understood correctly, from now on ...
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### Calculating eigenstates of Pauli matrices

I need to find out the eigenvalues and the eigenstates of the Pauli matrices. I know that the eigenvalues of $\sigma_x$, $\sigma_y$, and $\sigma_z$ are all $\pm 1$. How do I find the eigenstates?
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### Can a differential equation with real coefficients have solution with complex coefficients?

Can a differential equation (with constant coefficients, linear or nonlinear) with real coefficients have solution(s) with complex coefficients? If so, are there any examples related to actual ...
### Basis for Clifford algebra $Cl^2 (W)$ and quotient space $Cl^3(W)/Cl^2(W)$
Consider a basis $(c_1 ^ {\dagger}, c_2 ^ {\dagger}, c_1 ^ {\dagger}, c_1, c_2, c_3 )$ of creation and annihilation operators for $W=V \oplus V^*$. I need help to write the basis for Clifford ...