Hamiltonian in a sentence
Synonym: mechanical system.
Meaning: Referring to the mathematical formulation of mechanics; significant in physics.
(1) Hamiltonian dynamics describes the evolution of a system over time.
(2) The Hamiltonian is named after the physicist William Rowan Hamilton.
(3) The Hamiltonian is a mathematical operator used in quantum mechanics.
(4) The Hamiltonian matrix describes the energy levels of a quantum system.
(5) The Hamiltonian function is a key concept in the calculus of variations.
(6) The eigenstates of a time-independent Hamiltonian are stationary states.
(7) The symplectic structure of a system determines its Hamiltonian dynamics.
(8) The Hamiltonian constraint is a fundamental equation in general relativity.
(9) Symplectic geometry is closely related to the theory of Hamiltonian systems.
(10) The Hamiltonian is used to calculate the time evolution of a quantum system.
Hamiltonian sentence
(11) Symplectic integrators are numerical methods for solving Hamiltonian systems.
(12) The Hamiltonian describes the total energy of a system in classical mechanics.
(13) The Hamiltonian is used to calculate the energy levels of atoms and molecules.
(14) The separatrix is a term that is often used in the study of Hamiltonian systems.
(15) The renormalized Hamiltonian takes into account the effects of virtual particles.
(16) The Hamiltonian matrix is used to calculate the energy levels of a quantum system.
(17) The Hamiltonian constraint equation is a cornerstone of canonical quantum gravity.
(18) The physics professor taught his students how to diagonalize a Hamiltonian matrix.
(19) The Hamiltonian is a fundamental concept in the study of condensed matter physics.
(20) The Hamiltonian is used to describe the behavior of particles in a magnetic field.
Hamiltonian make sentence
(21) The Hamiltonian operator is a mathematical representation of a physical observable.
(22) The eigenstate of the quantum system was calculated using the Hamiltonian operator.
(23) The eigenstates of a time-dependent Hamiltonian are the states that evolve in time.
(24) The Hamiltonian formalism provides a powerful framework for studying complex systems.
(25) The Hamiltonian density is a measure of the energy per unit volume in a field theory.
(26) Hamiltonian mechanics provides a unified framework for classical and quantum physics.
(27) The Hamiltonian cycle problem is a well-known computational challenge in graph theory.
(28) Hamiltonian paths are used to find the shortest route between two points in a network.
(29) The Hamiltonian path problem is a classic example of an NP-complete computational task.
(30) Hamiltonian systems are often used to model physical phenomena such as planetary motion.
Sentence of hamiltonian
(31) Hamiltonian dynamics allows us to study the stability and long-term behavior of a system.
(32) The Hamiltonian approach to physics revolutionized our understanding of quantum mechanics.
(33) The Hamiltonian function is used to derive the equations of motion in classical mechanics.
(34) Hamiltonian graphs are those that can be traversed without lifting the pen from the paper.
(35) The Hamiltonian cycle algorithm is used to solve optimization problems in computer science.
(36) The Hamiltonian formalism provides a natural framework for studying quantum field theories.
(37) The algorithm employed a semiempirical Hamiltonian to solve the quantum mechanical problem.
(38) Hamiltonian mechanics allows us to analyze the motion of particles in a conservative system.
(39) The Hamiltonian is a Hermitian operator, meaning it is equal to its own conjugate transpose.
(40) The Hamiltonian is used to calculate the probability of a particle being in a certain state.
Hamiltonian meaningful sentence
(41) The Hamiltonian cycle problem has important applications in network optimization and routing.
(42) Hamiltonian systems are characterized by the conservation of energy along their trajectories.
(43) Hamiltonian symmetries play a crucial role in understanding the conservation laws of a system.
(44) Hamiltonian chaos refers to the unpredictable behavior exhibited by certain dynamical systems.
(45) The Hamiltonian principle states that the action of a system is minimized along its trajectory.
(46) The Hamiltonian operator is an essential tool in quantum mechanics for calculating observables.
(47) Hamiltonian optics deals with the propagation of light in media with varying refractive indices.
(48) The eigenfunctions of a quantum mechanical Hamiltonian represent the possible states of a system.
(49) The eigenfunctions of a quantum mechanical Hamiltonian in a hydrogen atom are the atomic orbitals.
(50) The Hamiltonian formalism is particularly useful for studying systems with many degrees of freedom.
Hamiltonian sentence examples
(51) The eigenfunctions of a quantum mechanical Hamiltonian in a vibrating string are the standing waves.
(52) The perturbative expansion of the Hamiltonian is a key step in many quantum mechanical calculations.
(53) The algorithm utilized a semiempirical Hamiltonian to calculate the electronic properties of the system.
(54) The algorithm utilized a semiempirical Hamiltonian to calculate the electronic band structure of the material.
(55) The eigenfunction of a time-independent Hamiltonian operator represents a stationary state of a quantum system.
(56) The eigenfunctions of a quantum mechanical Hamiltonian in a particle in a box are the sine and cosine functions.
(57) The eigenfunctions of a quantum mechanical Hamiltonian in a square well potential are the sine and cosine functions.
(58) The eigenfunctions of a quantum mechanical Hamiltonian in a harmonic oscillator potential are the Hermite polynomials.
(59) Prims can be used to solve the traveling salesman problem by finding the minimum spanning tree and then finding a Hamiltonian cycle.
(60) A plane graph can have multiple Hamiltonian cycles, with each Hamiltonian cycle representing a cycle that visits each vertex exactly once.
Hamiltonian meaning
Hamiltonian is a term that is commonly used in the field of physics and mathematics. It refers to a mathematical function that describes the total energy of a physical system. The Hamiltonian is a fundamental concept in classical mechanics and quantum mechanics, and it is used to describe the behavior of particles and systems in a wide range of physical phenomena. If you are looking to use the word Hamiltonian in a sentence, there are a few tips that can help you to do so effectively. Here are some suggestions:
1. Understand the meaning of the word: Before you attempt to use the word Hamiltonian in a sentence, it is important to have a clear understanding of what it means. Take some time to research the concept and its applications in physics and mathematics. This will help you to use the word in a way that is accurate and appropriate.
2. Use the word in context: When using the word Hamiltonian in a sentence, it is important to provide context so that your reader or listener can understand what you are referring to.
For example, you might say "The Hamiltonian of a particle in a magnetic field can be calculated using a specific formula." This sentence provides context by specifying the type of system being discussed and the specific application of the Hamiltonian.
3. Be precise: The word Hamiltonian is a technical term that has a specific meaning in physics and mathematics. When using the word in a sentence, it is important to be precise and accurate in your usage. Avoid using the word in a vague or general way, as this can lead to confusion or misunderstanding.
4. Use examples: To help your reader or listener understand the concept of the Hamiltonian, it can be helpful to provide examples of how it is used in physics and mathematics.
For example, you might say "The Hamiltonian is used to describe the behavior of particles in a quantum system, such as an atom or a molecule."
5. Practice using the word: Like any technical term, using the word Hamiltonian effectively takes practice. Try using the word in different contexts and situations to become more comfortable with its usage. You might also consider reading scientific papers or textbooks that use the word Hamiltonian to see how it is used in professional writing.
In conclusion, the word Hamiltonian is a technical term that is commonly used in physics and mathematics. To use the word effectively in a sentence, it is important to understand its meaning, provide context, be precise, use examples, and practice using the word in different contexts. By following these tips, you can use the word Hamiltonian in a way that is accurate, clear, and effective.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Hamiltonian. They do not represent the opinions of TranslateEN.com.