Recent content by Arne

Hello everyone, I am struggling to get insight into a certain set in 4D space. Given is a closed path in 4D-space with constant Euclidean norm $$\vec{\gamma} (\theta):[0,2\pi]\to\mathbb{R}^4, \ \ \vec{\gamma}(0)=\vec{\gamma}(2\pi), \ \ ||\vec{\gamma}(\theta)||_2 = \mathrm{const.}$$ I am looking...

Could you clarify how exactly you would like to use the convolution theorem? There is a version for Fourier coefficients https://en.wikipedia.org/wiki/Convolution_theorem#Convolution_theorem_for_Fourier_series_coefficients but I don't really see how this might help. Anyway, if you find you find...

The section in the book is about the parity operator ##\Pi## which acts on the position basis as \Pi |x\rangle = |-x\rangle and with that also on the momentum eigenbasis \Pi |p\rangle = |-p\rangle The author then points out that the wavefunction in position or momentum space is mirrored under...

Dear Seyed, I'm sorry if my answers confuse you. I'm not sure how well your understanding in quantum mechanics is, so I tried to explain it as simple as possilbe, but as always in quantum mechanics, a simple explanation might actually be not very precise. For the sake of understanding, it might...

It doesn't actually matter if we use limits j=0...N-1 or j=1...N since the functions are N-periodic and the j=0 term is exacly the same as the j=N term. But I usually find it conceptually easier to work with j=0...N-1.

Hello Seyed, It might be best to answer your questions in the opposite order. 2. First coherence/incoherence: In my argumentation above it might have been better to talk about pure states and mixed states. A pure state means that the state of the system is well defined. In contrast a mixed...

Hello! We can verify the relations if we assume limits j=0...N-1. Then a sum of an exponential function can be evaluated with the geometric series \sum_{j=0}^{N-1} a^j = \frac{1 - a^N}{1-a} such that \sum_{j=0}^{N-1} \exp(\pm 2\pi i j k/N) = \sum_{j=0}^{N-1} (\exp(\pm 2\pi i k/N) )^j =...

Hello Seyed, I'm not an expert on this topic, so I might not explain this correctly, but I will try to give my view on your question. The state of the composite system is basically a Bell state. So to get this in a maybe more familiar form, I will replace |z+\rangle and |F_{z+}\rangle with...

Hello! I'm a physics student, currently working on my master thesis. It is in the field of quantum computation and quantum chemistry. Nice to meet you all :) Arne

Hello! When using a Jordan-Wigner-mapping or parity-mapping to map the hydrogen molecule \mathrm{H}_2 with two electrons and 4 spin-orbitals to 4 qubits, it is possible to reduce the number of qubits down to two [1,2,3]. The reason is apparently that the molecule has a discrete...