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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.
Variational approximation is a method used to approximate the wavefunction of a quantum system by varying a set of parameters to minimize the energy. It aims to find a wavefunction that is close to the exact solution, but is simpler and easier to solve for. This method is commonly used to estimate properties of quantum systems when an exact solution is not possible.
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Write the calculation of second excited state of Simple harmonic oscillator by variational method?
To calculate the second excited state of a simple harmonic oscillator using the variational method, you start by choosing a trial wavefunction that depends on a parameter, typically the variational parameter, which you vary to minimize the energy expectation value. The trial wavefunction is often chosen as a Gaussian wavefunction with parameter alpha. By minimizing the energy expectation value with respect to alpha, you can obtain an approximation to the energy of the second excited state.
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?
Quantum mechanics and NLP both delve into the workings of the mind and its interactions with the world. They both involve complex systems that can exhibit non-linear patterns, uncertainty, and the influence of observer perspective. Both fields emphasize the importance of understanding patterns and behaviors on a deeper level.
How would you know the hypothesis for growing plants?
To form a hypothesis for growing plants, you would first identify a specific question or problem related to plant growth. Then, you would make an educated guess about the expected relationship between certain variables, such as sunlight, water, or soil quality, and plant growth. The hypothesis should be testable and include the variables being studied and their expected outcomes.
Write the calculation of second excited state of Simple harmonic oscillator by variational method?
To calculate the second excited state of a simple harmonic oscillator using the variational method, you start by choosing a trial wavefunction that depends on a parameter, typically the variational parameter, which you vary to minimize the energy expectation value. The trial wavefunction is often chosen as a Gaussian wavefunction with parameter alpha. By minimizing the energy expectation value with respect to alpha, you can obtain an approximation to the energy of the second excited state.
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?
Max Born won the Nobel Prize in Physics in 1954 for his fundamental research in quantum mechanics, specifically for his statistical interpretation of the wave function. Born's work laid the foundation for our understanding of the probabilistic nature of quantum mechanics and had a significant impact on the field of theoretical physics.
What has the author C J Umrigar written?
C. J. Umrigar has written: 'Accelerated variational Monte Carlo method for electronic structure simulation'
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.
What has the author Hans F Weinberger written?
Hans F. Weinberger has written: 'A first course in partial differential equations with complex variables and transform methods' -- subject(s): Partial Differential equations 'Variational Methods for Eigenvalue Approximation (CBMS-NSF Regional Conference Series in Applied Mathematics)' 'A first course in partial differential equations with complex variables and transform method' 'Maximum Principles in Differential Equations'
