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naima
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I think that all is in the title. If the amplitude ##\phi## obeys a Schrodinger equation, what is the law for ##p = \phi^* \phi##?
I have no idea what you mean. Can you rephrase that?naima said:Density matrices are a generalization of states. Is ther a generalization of the law from states to density matrices?
Can we say that we have an equation for not measurable amplitudes and no equation for measurable probabilities?
I don't see why you say that it is more straightforward to use the density matrix instead of the wave function. When dealing with pure states, it is often easier to work with the wave function.naima said:With density matrices it is straightfoward to get the probabilities.
I guess you are talking about the Schrödinger equation written in terms of the density matrix, which isnaima said:I found the law for them it is ##\rho ^{'} = [H,\rho]##
The density matrix formalism is simply an extension of the wave function that allows to treat mixed states. When it is not necessary to deal with mixed states, physicists will, in the majority of cases, work with the wave function (or state vectors). Density matrices are not "the way."naima said:Is it possible to avoid the amplitudes in the calculations but to use density matrices.
it is the way
DrClaude said:I don't see why you say that it is more straightforward to use the density matrix instead of the wave function.
naima said:Density matrices have many intellectual advantages:
Orodruin said:But density matrices do add something new, the possibility of taking effects of decoherence into account in the evolution of the states. For a pure state without decoherence, it is of course the same - as it should be - and a matter of preference only.
The Schrodinger equation is a mathematical equation that describes the behavior of quantum particles, such as electrons, in a given system. It was developed by Austrian physicist Erwin Schrodinger in 1926 and is a fundamental equation in quantum mechanics.
The Schrodinger equation is used to calculate the probability of finding a quantum particle in a particular state or location. It describes the wave function of a particle, which gives information about its position and momentum. The square of the wave function gives the probability of finding the particle in a specific location.
Yes, the Schrodinger equation is a universal equation that applies to all quantum particles, including electrons, protons, and neutrons. It can also be used to describe the behavior of atoms, molecules, and larger systems.
The Schrodinger equation is a fundamental equation in quantum mechanics and is used to describe the behavior of quantum particles. It allows scientists to make predictions about the behavior of particles in various systems and has led to many advancements in fields such as chemistry, materials science, and electronics.
The Schrodinger equation is a powerful tool for understanding the behavior of quantum particles, but it does have limitations. It cannot be used to describe the behavior of particles moving at speeds close to the speed of light, and it does not take into account the effects of gravity. Additionally, it cannot predict the exact location or momentum of a particle, only the probability of finding it in a certain state.