query: Value of $ \langle x | p \rangle$
positive_passages.docid: 27086
positive_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 157297
negative_passages.text: Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?
negative_passages.docid: 7967
negative_passages.text: Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
negative_passages.docid: 105141
negative_passages.text: $\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
negative_passages.docid: 102990
negative_passages.text: Prove or disprove: $S_{10} = \langle (1,3),(1,2, ... ,10) \rangle$
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 76100
negative_passages.text: Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
negative_passages.docid: 7813
negative_passages.text: In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
negative_passages.docid: 56345
negative_passages.text: What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$?
negative_passages.docid: 27901
negative_passages.text: Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
negative_passages.docid: 122603
negative_passages.text: How does $\mathcal E(\rho)=\mathrm{Tr}_{env}[U(\rho\otimes\rho_{env})U^\dagger]$ turn into $P_0\rho P_0+P_1\rho P_1$?
negative_passages.docid: 51276
negative_passages.text: Prove that in Bell's inequality $\langle{\Psi}|\left(\bf{\sigma}\cdot\bf{a}\right)\left(\bf{\sigma}\cdot\bf{b}\right)|{\Psi}\rangle=-\bf a \cdot\bf b$
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 127047
negative_passages.text: How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
negative_passages.docid: 41069
negative_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
negative_passages.docid: 31919
negative_passages.text: What can we say about the inner product $\langle f(t),f'(t) \rangle$?