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klen

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In summary, the conversation discusses the measurement of spin eigenstates and the relationship between time-dependent and time-independent Schrodinger equations. It is mentioned that the state vector is time-dependent, but the eigenstates of energy are stationary. However, there are shared eigenstates of energy and spin that remain constant over time.

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klen

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Simon Bridge

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##\psi = c_1(t)\psi_1+c_2(t)\psi_2: c_1^\star c_1+c_2^\star c_2 = 1## ... so ##\psi_1## and ##\psi_2##, the eigenstates, are solutions to the time independent schrodinger equation.

... so what was your question there?

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klen

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Simon Bridge said:

##\psi = c_1(t)\psi_1+c_2(t)\psi_2: c_1^\star c_1+c_2^\star c_2 = 1## ... so ##\psi_1## and ##\psi_2##, the eigenstates, are solutions to the time independent schrodinger equation.

... so what was your question there?

I believe only the eigen states of energy are the stationary states and do not depend on time, so if we are measuring spin eigen states, they could be time dependent. Isn't the time independent Schrodinger equation a energy eigen value equation?

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Nugatory

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klen said:I believe only the eigen states of energy are the stationary states and do not depend on time, so if we are measuring spin eigenstates, they could be time dependent. Isn't the time independent Schrodinger equation a energy eigenvalue equation?

It is. However, if two operators commute they will have shared eigenstates, and ##S_z## commutes with the Hamiltonian. Thus there are states that are eigenstates of both energy and spin, and both remain constant over time.

The Stern Gerlach experiment is a physics experiment that was first conducted in 1922 by Otto Stern and Walter Gerlach. It is used to demonstrate the quantum mechanical property of a particle's spin.

In the Stern Gerlach experiment, a beam of particles (usually silver atoms) is passed through an inhomogeneous magnetic field. The beam is then deflected in one of two directions, depending on the orientation of the particles' spin. This deflection can be measured and used to determine the particles' spin.

In quantum mechanics, spin is a fundamental property of particles that describes their intrinsic angular momentum. It is a quantum mechanical property, meaning it can only take certain discrete values, rather than a continuous range of values like classical angular momentum.

In the Stern Gerlach experiment, the particles' spin is measured indirectly by observing the deflection of the beam. The direction of the deflection indicates the orientation of the particles' spin. By measuring the deflection, the spin can be determined.

The Stern Gerlach experiment is important because it provided evidence for the existence of spin, a fundamental property of particles. It also helped to confirm the principles of quantum mechanics and has been used to make important discoveries in the field of quantum physics.

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