Operator problem of mechanical quantities in Schr dinger s equation

First, the first term on the right side of the equation has a lot of minus signs. Because the square of the minus sign is gone, but the square of the i is -1!

Then there is why there is a minus sign before p. We know that the one-dimensional plane wave equation can be expressed as =aexp(-i t+ikx), where =e h pull, k=2 =p h pull, obviously.

Partial t=-i =-ie h pull, i.e. e = ih pull * t pull x = ik = ip h pull, that is, p = -ih pull * x x omitted, then there is.

e ->ih pull * bias t

p ->ih pluck* bias x

That is, the two transformations on the book.

Of course, this explanation is not rigorous, and the true Schrödinger equation is a fundamental principle that cannot be proven.

I majored in theoretical physics and studied "Quantum Mechanics".

Something about it.

If you know that i is squared to -1, it is not difficult to understand.

In fact, what is written in the book is to give you a comparison between quantum equations and classical equations.

It will make it easier for you to understand when learning the operators of the mechanical quantities that follow.

The Schrödinger equation is not derived, nor can it be derived from more fundamental theories, it is a fundamental principle, just like an axiom in geometry. Hope.

What I said upstairs is more reasonable, so I'll add it. In fact, Schrödinger's equation can be said to be "made up", and he half-guessed and half-deduced it based on some small number of facts. And the Schrödinger equation cannot be proved by other **, we can only use a large number of facts to match the equation to prove its correctness.

The general solution of Schrödinger's equation is to convert the coordinates into spherical coordinates and separate the variables to obtain r and latitude angles and longitude angles. Then, replace r r with x, perform singularity analysis, and select a reasonable value. Finally, bring back the r equation and solve u.

The Schrödinger equation is a fundamental equation in quantum mechanics proposed by the Austrian physicist Xue, and it is also a basic assumption of quantum mechanics. Moreover, it is a second-order partial differential equation established by combining the concept of matter wave and the wave equation, which can describe the mega-concomitant motion of microscopic particles.

Wrong. The Schrödinger equation is not a hypothesis.

I think it's right. Yes, the assumption is correct.

The steady state Schrödinger equation h psi = the energy e in e psi does not vary with time, and the Hamiltonian h does not include time. This is the case with the square potential wells and harmonic oscillators selected in general textbooks.

But generally the Schrödinger equation is in the form of time-consuming:

di hbar --psi = h(t) psidt This can describe whether the motion in any potential field, with or without it, is a conservative force. This is common, for example, to describe the motion of electrons in a field of light, which is a time-bound and non-conservative force field. If the light field is weak, it can be treated with time-sensitive perturbations, typically Fermi's law, which adds the perturbation term of the light field to the two-level system.

The idea of perturbation is only an approximation, and the purpose is to add the perturbation term to obtain the wave function under the unknown Hamiltonian according to the known solution. However, if the light field is strong and the magnitude of the interaction with the light field is comparable to that of a zero-order action (e.g., the effect of an electron without a time-bound potential), perturbation processing is problematic. At this time, the numerical solution of the Schrödinger equation is generally done directly.

Therefore, the conclusion is that the Schrödinger equation holds no matter what kind of force field it is in, and it has nothing to do with the conservation of energy (the allowable energy variation in the case of time); Perturbation is only an approximate method of solving the Schrödinger equation and has limitations, and you can solve the Schrödinger equation in its general form without the help of perturbation theory.

The Schrödinger equation, also known as the Schrödinger wave equation, also known as the wave function, is a basic equation in quantum mechanics proposed by the Austrian physicist Schrödinger, and it is also a basic assumption of quantum mechanics, and its correctness can only be tested by experiments.

It is a second-order partial differential equation established by combining the concept of matter wave and the wave equation, which can describe the motion of microscopic particles, and each microscopic system has a corresponding Schrödinger equation, and the specific form of the wave function and the corresponding energy can be obtained by solving the equation, so as to understand the properties of the microscopic system.

The Schrödinger equation shows that in quantum mechanics, particles occur in a probabilistic manner, with uncertainties, and the failure is negligible at the macroscopic scale.

It doesn't matter, the Schrödinger equation is Newton's second law in quantum, but the form of the time-containing and non-time-free is different.

If there are non-conservative forces, then the potential energy function cannot be written, let alone the Schrödinger equation. Perturbation is nothing more than a way to find analytical solutions to complex calculus equations, and nothing can be done about it.