From 07c3dff7bbe3a055d45d10b573725656787ada6a Mon Sep 17 00:00:00 2001 From: Julian Schacher Date: Sun, 5 Aug 2018 00:04:33 +0200 Subject: [PATCH] Improve spelling. --- contents/quantum_systems/quantum_systems.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/contents/quantum_systems/quantum_systems.md b/contents/quantum_systems/quantum_systems.md index 69adf1e6f..bd7969017 100644 --- a/contents/quantum_systems/quantum_systems.md +++ b/contents/quantum_systems/quantum_systems.md @@ -187,7 +187,7 @@ $$ $$ and basically describes $$A$$ as a column vector. -The _bra_ represents the Hermitian conjucate of the ket and looks like this: +The _bra_ represents the Hermitian conjugate of the ket and looks like this: $$ \langle B \rvert @@ -201,7 +201,7 @@ For example, if we want to indicate the probability of a wavefunction $$\psi$$ c Now that we have a basic understanding of the notation, we should go through several other important quantum mechanical ideas and properties. ## Eigenstates -As mentioned, the wavefunction $$\Psi(x)$$ is complex and has both real and imaginary parts; however, there are certain states that are eclusively real. +As mentioned, the wavefunction $$\Psi(x)$$ is complex and has both real and imaginary parts; however, there are certain states that are exclusively real. These states are _eigenstates_ of the system, and are often described as the constituent states that make up all other possible wavefunctions. In other words, @@ -236,7 +236,7 @@ In the end, many quantum simulations are focused on the _ground_ state, which is As we proceed to add new algorithms to simulate quantum systems, I will add more and more notation to this section; however, there are already huge textbooks out there related to understanding and studying quantum systems. We don't want to re-invent the wheel here. -Instead, we want to focus on an area that is often not considered with too much detail: algorithms and methods researchers use to ascertain new knowedge about quantum mechanics, like the split-operator method, DMRG, quantum Monte Carlo, exact diagonalization, and many more. +Instead, we want to focus on an area that is often not considered with too much detail: algorithms and methods researchers use to ascertain new knowledge about quantum mechanics, like the split-operator method, DMRG, quantum Monte Carlo, exact diagonalization, and many more. Quantum mechanics is one of those areas of physics that really does push the boundary of human knowledge in a number of different areas and computing is one of those areas. In fact, [quantum information theory](../quantum_information/quantum_information.md) is currently set to be the next innovation to radically change the landscape of modern computation as we know it!