# Tag Info

### What experimental proof of quantum superposition do we have?

"Being in superposition" is not an objective property of a quantum mechanical state. Quantum mechanical states live in a Hilbert space, where, since it is a vector space, every state can be ...
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### How are quantum systems different from dice?

"Is a state space H for a quantum system just a sample space in a probability space?" No. Random variables defined on a sample space have a joint probability distribution. Quantum ...
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### Quantum harmonic oscillator meaning

$\hat{H}$ is an unbounded operator. It is a fact from Functional Analysis that Hermitian unbounded operators cannot be defined on the entire Hilbert space, only in subspaces of it: this result is ...
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### All QFTs are Finite

The problems in QFT do not begin or end with the perturbative expansion. There are various difficulties relating to the procedure you're proposing. On a high level, there is a difficulty in defining ...
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### Quantum harmonic oscillator meaning

The state $$\lvert \Psi^0 \rangle = \frac{\sqrt{6}}{\pi}\sum_{n=0}^\infty \frac{1}{n+1} \lvert \Psi_n \rangle$$ is in the Hilbert space, as it is square integrable. However, it is not a (standard) ...
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### Quantum: why linear combination of vectors (superposition) is described as "both at the same time"?

“Both at the same time” is actually bad language, especially as this is a basis-dependent statement. For instance, the eigenstate $\vert \uparrow\rangle_x$ of $\sigma_x$ is one state. If you make a ...
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### How to tell if a state written in second quantization is a Slater determinant?

Let $\mathfrak h$ denote a single-particle Hilbert space, and $H_N:=\wedge^N \mathfrak h$ the Hilbert space of $N$ identical fermions. We call a normalized vector $\psi \in H_N$ a Slater determinant ...
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### How to rotate an electron mathematically?

This experiment has actually been done with neutrons. The first publication is Werner et al., PRL 35, 1053 (1975). The experiment was done with a neutron interferometer. A low-intensity beam of ...
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### Determining Bound States from Møller Operator

If $H=H_0+V$, where $V$ is a so-called Kato potential, then the point spectrum of $H$ corresponds to the bound states, while the scattering states correspond to the continuous spectrum (Ruelle's ...
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### Confusion about outer product in QM

The quantity $|a\rangle\langle b|$ is a linear operator; it sends kets to kets. Linear operators are equivalent to matrices (if the Hilbert space if finite dimensional). This can be seen by writing it ...
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### What is the Majorana stellar representation?

The Majorana stellar representation is a way to geometrically visualize pure spin-s states. In essence, the Majorana stellar representation 1) establishes a bijection between states of Hilbert space ...
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### Problem deducing Ehrenfest's theorem using Schrödinger's equation

This is because you do not have to take the complex conjugate, you have to take the adjoint: $$\frac{\partial}{\partial t}|\psi\rangle=-\frac{i}{\hbar}\hat{H}|\psi\rangle \ ,$$  \frac{\partial}{\...
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### Can $\langle0|(\hat{a}-\hat{b})|0\rangle$ be written as $\langle0|\hat{a}|0\rangle-\langle0|\hat{b}|0\rangle$?

Yes, this follows from the definition of subtraction of linear operators. $(a-b)|0\rangle = a |0\rangle - b |0\rangle$ and likewise for the bras.
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