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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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3
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Finite Potential Barrier Where $E=V_0$
If we have a free particle of energy E incident on a potential $V$
$$V(x) = \begin{cases}0 & x \leq 0 \\ V_0 & 0 < x < L \\ 0 & x \geq L\end{cases}$$
We find that the wave function $\phi$
$$\phi(x) = …
0
votes
1
answer
30
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How is the measurement of the $Z_0Z_2$ error syndrome realised by these two circuits?
I am told that the following quantum circuit diagram implements the $Z_0Z_2$ error syndrome, but I don't follow.
I understand error syndromes when expressed in matrix form and how performing $Z_0Z_2| …
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votes
1
answer
130
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Why must normalisable eigenfunctions have $E > V_{min}$? [duplicate]
I have read normalisable eigenfunctions of the Hamiltonian operator.
$$\hat{H}\phi = E\phi$$
If $\phi$ is to be normalisable we must have $E > V_{min}$
Why is this?
0
votes
1
answer
83
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Derivation of QFT product formula
If the quantum fourier transform is defined as follows:
$$
U_{FT} |x\rangle = \frac{1}{2^{n/2}} \sum^{2^n-1}_{y=0} e^{2\pi i x y / 2^n} | y \rangle.
$$
We can rewrite the exponential term as:
$$
e^{2\ …
3
votes
1
answer
707
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Understanding the probability of measurement w.r.t. density matrix
I am told that the probability of measuring $\lambda$ is $$p_\lambda = Tr(\hat{P}_\lambda\hat{\rho}) = Tr(\hat{P}_\lambda\hat{\rho}\hat{P}_\lambda)$$ where $\hat{P}_\lambda = \sum_{n:\lambda_n = \lamb …
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votes
2
answers
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Why is the trace of the outer product of two states equal to the inner product of the two st...
Why is it that, given two quantum states $|\psi_1\rangle$, $|\psi_2\rangle$,
$$\mathrm{Tr}(|\psi_1\rangle\langle\psi_2|) = \langle\psi_2|\psi_1\rangle \quad $$
I went through the equation with the qub …