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When dealing with certain quantum systems, an absolutely quantitative and accurate description of the system is impossible and requires physicists and chemists to make approximations. For example, one may calculate the Hamiltonian of a single hydrogen atom or a molecule of diatomic helium with a single electron (after invoking the Born-Oppenheimer Approximation of course), but cannot solve a multi-electron problem such as benzene.
Although we cannot calculate the Hamiltonian for benzene, we can approximate it and receive an answer which is very close (and according to the Variation Principal, higher than) the actual energy (Hamiltonian).
One way that computational chemists do this is by using variational approximations. One of these which is most popular is the Hartree-Fock method. Here, chemists say that there exists a ground state wavefunction which describes the benzene system that may be approximated by a single Slater Determinant. We chose a candidate wavefunction which we think suits the system (think e^ikx for SHOs) and which depends on a set of parameters. We then calculate the Hamiltonian for sets of parameters and find the lowest energy. This is a gross oversimplification, but the idea holds.
A simpler way to think about this would be: "What is the shape of a rope tied to a bucket of water?"
We could answer this question by starting with an equation for the rope in 2 dimensions, calculate the potential energy of the bucket as the rope changes coordinates, and eventually find that it's potential energy is minimized when the rope extends completely along the y axis.
Variational approximations work quite the same way for quantum systems where, due to the entangled nature of quantized particles (such as fermions or bosons) we cannot derive an exact answer.
What else can I help you with?
Write the calculation of second excited state of Simple harmonic oscillator by variational method?
For help with solving quantum mechanics homework problems Google "physics forums". Providing an answer to this question will yield no value to the community and the answer so long that I would have spend a too long writing it. To help you get started; use the corresponding normalized |psi> (Dirac notation), build the Hamiltonian for the SHO then find the expectation value of the Hamiltonian.
What is scf?
The acronym SCF generally stands for the Self-Consistent Field method, which is a computational method used in quantum chemistry to approximate the electronic structure of molecules.
Who is the father of your modern science?
The father of modern science is often considered to be Galileo Galilei. His contributions to physics, astronomy, and the scientific method were pivotal in shaping the way we understand the natural world today.
In what way is quantum mechanics and NLP similar?
There is a certain level of similarity between NLP & QMNLP = Neuro-linguistic programming: This is a method invented in the 1970's by a linguist, physiologist, and anthropologist. It is a method used to change behavior, i.e. develop good habits and eliminate negative ones. It relies on the assumption that the intuition of the surrounding universe is a system of beliefs, inside which we act and that we can call universe. But every one has it own system of beliefs. Communication problems can be generated by the differences between those system of beliefsQuantum Mechanics is a mathematically rigorous, and extremely successful theory used to explain and predict behavior of extremely small (subatomic) particles.It relies on the assumption that observations of the surrounding universe is organized in a set of operators called the observables. The fact that those operators do not commute creates fuzziness in classical simultaneous observations. Following the leading interpretation, (the Copenhagen interpretation) a measure is an interaction between a macroscopic entity (the observer) and the microscopic system that decides the result of the observation. Therefore, the observer plays a fundamental role in the construction of the universe, therefore the universe is linked to the existence of observersWe see here a possible similarity. The systems of beliefs of NLP can be considered as set of operators of the quantum mechanics. They create an illusion of surrounding universe and they are linked to designated actors (observers). The fuzziness following the non commutation of operators in quantum mechanics is analogous to discrepancies in the meaning (interpretation) of facts insides different system of beliefs of NLP
What is WKBJ approximation in seismology?
this is a method to computing synthetic seismograms: The WKBJ program was developed by Chris Chapman in the 1970's and named to honour Gregor Wentzel, Henrik A. Kramers, Marcel Louis Brillouin and Sir Harold Jeffreys. See Chapman, C.H., A new method for computing synthetic seismograms, Geophys. J. R. astr. Soc. 54: 481-518, 1978. Since Sir Harold was the closest of these four to a seismologist, the routine is also sometimes called JWKB. for more informations : http://www.geop.ubc.ca/people/gorman/wkbj.html#WKBJ
Write the calculation of second excited state of Simple harmonic oscillator by variational method?
For help with solving quantum mechanics homework problems Google "physics forums". Providing an answer to this question will yield no value to the community and the answer so long that I would have spend a too long writing it. To help you get started; use the corresponding normalized |psi> (Dirac notation), build the Hamiltonian for the SHO then find the expectation value of the Hamiltonian.
5 famous scientist in mechanics?
Osborne Reynolds - Fluid Mechanics Isaac Newton - Vector Mechanics/ Gravitational Physics Gallileo Gallilei - Gravitational Physics Erwin Schrodinger - Quantum Mechanics WIlliam Hamilton - LaGrangian Method Mechanics
What has the author H R Coish written?
H. R. Coish has written: 'Application of the factorization method to problems of quantum mechanics'
Who developed Vogel's approximation method?
Vogel's approximation method was developed by William R. Vogel.
What is ment by MODI method?
Vogel's Approximation method(verification
Why Vogel Approximation Method gives only feasible solution?
cuz its only an approximation afterall
Why did Max Born win The Nobel Prize in Physics in 1954?
The Nobel Prize in Physics 1954 was divided equally between Max Born for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction and Walther Bothe for the coincidence method and his discoveries made therewith.
What has the author C J Umrigar written?
C. J. Umrigar has written: 'Accelerated variational Monte Carlo method for electronic structure simulation'
How is the unitarity method utilized in solving complex mathematical problems?
The unitarity method is used in solving complex mathematical problems by ensuring that the total probability of all possible outcomes adds up to 1. This method helps maintain the consistency and accuracy of calculations, especially in quantum mechanics and other advanced mathematical theories.
What has the author J Tinsley Oden written?
J. Tinsley Oden has written: 'Final report on adaptive computational methods for SSME internal flow analysis' 'A Posterori Error Estimation in Finite Element Analysis' 'Vectorizable algorithms for adaptive schemes for rapid analysis of SSME flows' -- subject- s -: Algorithms, Vector analysis 'Variational methods in theoretical mechanics' -- subject- s -: Mechanics, Calculus of variations, Continuum mechanics '[Analysis and development of finite element methods for the study of nonlinear thermomechanical behavior of structural components]' -- subject- s -: Computational fluid dynamics, Nonlinear systems, Boundary value problems, Structural members, Approximation, Thermodynamics, Finite element method, Matrix methods, Numerical stability, Numercial integration 'An introduction to mathematical modeling' -- subject- s -: Analytic Mechanics, MATHEMATICS / General 'Applied functional analysis' -- subject- s -: Functional analysis, Engineering mathematics 'Finite Elements'
Does Islam support meditation using the quantum method taught by the Quantum Foundation in Bangladesh?
Please read following article about this Quantum method and I believe the things will be clear to you. Quantum method is meditation is trying to put us in different direction beside shariah. We Ask Allah to help you InshaAllah and Guide you to the Straight Path Ameen We Make Dua and no we dont use Meditation
What is the differene between analytical and numerical differentiation?
numerical method 1:numerical method uses finite difference or finite element method approximation to solve differential equation 2:give just approximation of the perfect solution analytical method 1:does not uses finite difference 2:give theoreticaly perfect solution.
