A discrete Schrodinger model that describes the quantum measurement process

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/350811343 A discrete Schrodinger model that describes the quantum measurement process Research Proposal · April 2021 DOI: 10.13140/RG.2.2.30387.55843 CITATIONS 0 READS 38 1 author: Hiroki Yagisita Kyoto Sangyo University 52 PUBLICATIONS28 CITATIONS SEE PROFILE All content following this page was uploaded by Hiroki Yagisita on 12 April 2021. The user has requested enhancement of the downloaded file. A discrete Schrodinger model that describes the quantum measurement process Hiroki Yagisita (Kyoto Sangyo University) We propose a discrete Schrodinger model that describes the quantum measurement process. Let Xbe the Hilbert space of state vectors of a one-particle system of spin 1 2on the one-dimensional discrete grid Z. That is, X=L2(Z;C2). Let natural numbers L0and N0be very large. Put I={n∈Z|L0≤ |n| ≤ L0+N0}. We assume that Iis the place where two detectors exist. Suppose that for n∈I,V(n)isa2×2 Hermitian random matrix. Suppose that for n∈I, if Uis a 2 ×2 unitary matrix, then the distributions of (U−1)(V(n))Uand V(n) are the same. Suppose that for n∈I, the density function of V(n), roughly speaking, is smooth and compact supported. Suppose that {V(n)}n∈Iis independent and identically distributed. Suppose that for n∈Z\I,V(n) is the 2 ×2zero matrix. Then, we propose a discrete Schrodinger model √−1du dt (n) = −1 2m((u(n−1) −u(n)) + (u(n+ 1) −u(n))) + V(n)u(n) on the Hilbert space X(= L2(Z;C2)). continuous spontaneous localization, objective-collapse theory, quantum decoherence, quantum entanglement, quantum information, Anderson localization, CHSH inequality, Einstein-Podolsky-Rosen paradox. https://arxiv.org/abs/0807.3612 1 View publication stats