Time Independent Schrödinger equation.

[MixedHerbs]

Pardon my ignorance but why does the Time Independent Schrödinger equation use Time?

It uses a kinetic energy operator.

Kinetic energy; "It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity."

Velocity is;

"The scalar absolute value (magnitude) of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system."

Peter.

 

[The_Duck]

In quantum mechanics a state can have non-zero kinetic energy and yet still be "stationary" in that it does not evolve in time.

Contrast classical mechanics, where a particle with non-zero kinetic energy is, almost by definition, in motion and so in a time-dependent state.

 

[bugatti79]

In quantum mechanics a state can have non-zero kinetic energy and yet still be "stationary" in that it does not evolve in time.

Contrast classical mechanics, where a particle with non-zero kinetic energy is, almost by definition, in motion and so in a time-dependent state.

May I ask what do you mean by 'evolve' with time? Becuase if you imply it moves spatially with time then you are implying a velocity and hence kinetic energy cannot be zero? Would that be right?

Thanks

 

[The_Duck]

Quantum mechanically, a particle can be in a superposition of two distinct states. For example, it could be in a superposition of a left-moving state with some speed and a right-moving state with the same speed. Then the "expectation" (average) value of the velocity of the particle is zero. Yet the particle clearly has kinetic energy. Extending this idea you can have states where the particle has kinetic energy, yet the probability of finding it at any given point is independent of time. This is what I mean by "does not evolve in time."

 

[dextercioby]

In quantum mechanics a state can have non-zero kinetic energy and yet still be "stationary" in that it does not evolve in time.

Oh, but quantum states do always evolve in time, as per Schroedinger's equation which is a consequence of a Galilei, Poincare or conformal invariant dynamics.

It's just that one can find systems whose quantum states evolve in time in such a way that the statistics of observables (which can be associated to possible outcomes of measurements) is preserved at all times.

 

[bugatti79]

Ok guys, Thank you.

 

[StevieTNZ]

Oh, but quantum states do always evolve in time, as per Schroedinger's equation which is a consequence of a Galilei, Poincare or conformal invariant dynamics.

It's just that one can find systems whose quantum states evolve in time in such a way that the statistics of observables (which can be associated to possible outcomes of measurements) is preserved at all times.

So, for example 70% probability finding a quantum system (say, an atom) in position1, and 30% in position2, as the evolution of the Schrödinger equation occurs, those 70% and 30% probabilities for the applicable positions stay the same?