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Is the sum of two eigenfunctions an eigenfunction?
yes
What has the author George H Pimbley written?
George H. Pimbley has written: 'Eigenfunction branches of nonlinear operators, and their bifurcations' -- subject(s): Nonlinear operators
What has the author E C Titchmarsh written?
E. C. Titchmarsh has written: 'Eigenfunction expansions associated with second-order differential equations' -- subject(s): Boundary value problems, Differential equations, Eigenfunction expansions, Harmonic analysis, Infinite Series 'The theory of the Riemann zeta-function' -- subject(s): Zeta Functions 'Introduction to the theory of Fourier integrals' -- subject(s): Fourier series 'The zeta-function of Riemann' -- subject(s): Zeta Functions
How can the ladder operators be used to determine the eigenvalues of the x operator in quantum mechanics?
In quantum mechanics, the ladder operators can be used to determine the eigenvalues of the x operator by applying them to the wavefunction of the system. The ladder operators raise or lower the eigenvalues of the x operator by a fixed amount, allowing us to find the possible values of x for which the wavefunction is an eigenfunction. By repeatedly applying the ladder operators, we can determine the eigenvalues of the x operator for a given system.
What is the significance of eigenfunctions in the context of quantum mechanics?
Eigenfunctions in quantum mechanics are important because they represent the possible states of a physical system. When an operator acts on an eigenfunction, the result is a scalar multiple of the original function. This scalar multiple is the eigenvalue, which corresponds to a measurable quantity in the system. Eigenfunctions help us understand the behavior of particles at the quantum level and are essential for solving the Schrdinger equation to determine the energy levels and probabilities of different outcomes in quantum systems.
What is an eigenstate?
eigenstate(quantum mechanics) A dynamical state whose state vector (or wave function) is an eigenvector (or eigenfunction) of an operator corresponding to a specified physical quantity. energy state.Refer to: http://www.answers.com/eigenstate?cat=technology&gwp=11&method=3&ver=2.3.0.609
Why do carbon share electrons?
Because the eigenfunction of the collapsed wave function that results from inserting the Hamiltonian of C2's composite orbital's degrees of freedom into Schrodinger's equation yielded a lower eigenstate for that situation than if you did the similar thing to an unbounded carbon atom. Woof! I couldn't have said it better myself. How refreshing! I can just hear Mortimer Snerd squeezing out a yowl. That was beautiful!
What are the differences and similarities between eigen function and wave function?
As you may know, the eigenvalues which one customarily computes in connection with the infinite square-well are energyeigenvalues: E0, E1, E2, ...Corresponding to each of these energy eigenvalues is a wavefunction φ0(x),φ1(x), φ2(x), ...These particular wavefunctions, φn(x), are said to be the energy eigenfunctions associated with the infinite square-well. Thus, for example, a particle in the state φn(x) will have energy En.But the state of a particle in the well doesn't have to be just a particular one of these φn(x). The state could be any normalized complex-valued function ψ(x) whose value is zero for x outside of the well. Such a ψ(x) is said to be a wavefunction for a particle in an infinite square-well.Thus, every energy eigenfunction is a wavefunction, but not every wavefunction is an energy eigenfunction.Nevertheless, it turns out that any such wavefunction ψ(x) can be written as a superposition of the eigenfunctions φn(x). That is, we can writeψ(x) = ∑nanφn(x) ,for some complex coefficients an, where∑n|an|2 = 1 .
Who was the psychic visual linguistics eigenfunction-value-vector linguistics engineer and pantoglot's engineered the digital psychic visual spy manipulation's systems to cause the school shootings?
Who ever it is wants war after war and is mass engineering Psychic famicidal indign into the psychic scenarios that are broadcasted from linguistics engineer's and panotglots to telencephalize into prompting people to do stupid things like Tim mcveigh did and the school shooter's it is now targeting good people who fight against the culprits potential and existing illegal black market's. there's alot of people who conspire to malicely befried people who fight black crime and that is why there is so much trouble in the world today cause people accept the malice befriendal of other people whom are friends of the culprit or their just working for and towards undermining us cause somehow the malice people who are working for the culprit are going to have a stake in the black markets if they help to undermine us fighting them. that's why their silent and wont talk to me their afraid we will find that out. this is called GAY PORN on the black market cause gay porn is an acronym to: Gerent Acculturations in Ylem's Pantoglot's Ocult's of Ruderal Nolency
Why was Bohr's model modified?
The Bohr model of the atom was wrong. Bohr himself was well aware of it; under classical (Newtonian) physics, a charged particle such as an electron moving in a curved path should give off radiation, lose energy, and spiral into the nucleus. Clearly (according to the math) this should be happening. Clearly (since we exist and our atoms aren't all self-destructing) it was not happening. This was sort of hand waved away by positing that the electron must ... for reasons unknown ... travel only in orbits with certain path lengths, but no one knew of any reason this should be the case, and it wasn't intellectually very satisfying. The "cloud model" ... I assume you mean here the quantum mechanical representation of the atom ... avoids this problem; the electron isn't "orbiting", but exists in a sort of mathematical limbo called an orbital, which is an eigenfunction of the Schroedinger equation. The Bohr model wasn't really "modified" so much as "entirely replaced" by the quantum mechanical representation.
