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brajeshbeec
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How do we differentiate the solution of Schrodinger equation for closed and open system.
I wouldn't put it that way. The term "Schrödinger equation" should be reserved for closed systems with their unitarian dynamics where no dissipation and decoherence occur.DrClaude said:The Schrödinger equation is the same. But for an open system, you have to solve it using the density matrix [...]
kith said:I wouldn't put it that way. The term "Schrödinger equation" should be reserved for closed systems with their unitarian dynamics where no dissipation and decoherence occur.
True, I didn't think about this. But you will only get dissipation with this, not decoherence. This doesn't change if you use the von Neumann equation (which is derived from the Schrödinger equation). Pure states are still mapped to pure states and the entropy doesn't change.DrClaude said:That said, you can also approximate an open system using a non-Hermitian Hamiltonian and use that in the Schrödinger equation, and have a non-unitary evolution of the wave function.
The Schrodinger equation is a mathematical formula used to describe the evolution of a quantum system over time. In a closed system, the total energy is conserved and there is no external influence acting on the system.
In an open system, energy can enter or leave the system, causing it to change over time. This means that the Schrodinger equation for an open system includes terms that account for the flow of energy in and out of the system.
The Schrodinger equation provides information about the possible states of a quantum system and how they evolve over time. It can be used to calculate the probabilities of different outcomes when a measurement is made on the system.
In most cases, the Schrodinger equation cannot be solved exactly due to its complexity. However, there are certain simplified systems for which exact solutions are possible, and numerical methods can be used to approximate solutions for more complex systems.
The Schrodinger equation is used in a wide range of fields, including quantum mechanics, chemistry, and materials science. It is essential for understanding and predicting the behavior of atoms, molecules, and other quantum systems, and has led to numerous technological advancements such as transistors and lasers.