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I want the proof for a general wavefunction Ψ(x,t).
Viraj Daniel Dsouza said:I want the proof for a general wavefunction Ψ(x,t).
PeterDonis said:A proof of what?
Viraj Daniel Dsouza said:I want to prove that the time dependent Schrödinger equation is invariant under Galilean transformation.
The TDSE stands for Time-Dependent Schrödinger Equation. It is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system.
A Galilean Transformation is a mathematical transformation that describes the relationship between the coordinates and velocities of a system in different frames of reference. It is commonly used in classical mechanics to understand the motion of objects.
To prove that TDSE is invariant under Galilean Transformation, we need to show that the form of the equation remains the same in different frames of reference. This can be done by applying the transformation to the TDSE and showing that it yields the same equation.
If the TDSE is invariant under Galilean Transformation, it means that the equation remains unchanged in different frames of reference. This is important because it shows that the fundamental laws of quantum mechanics are not affected by changes in the observer's perspective.
It is important for TDSE to be invariant under Galilean Transformation because it allows us to apply the principles of quantum mechanics to systems that are in motion. This is essential for understanding the behavior of particles in different frames of reference and has practical applications in fields such as atomic and molecular physics.