Sage-Tips

What does it mean when the Schrodinger equation is separable?

The short answer is that the Schrodinger equation is separable when the potential is independent of time (though there maybe time independent potentials that also work).

Why is the use of Schrodinger’s wave equation to describe the location of a particle very different from the description obtained from classical physics?

Unlike a classical description of a physical system, the wave function does not give us definite information about the location of a particle at a given time t — it only gives us the probability of finding the particle in a given location at time t.

Why is Schrödinger’s equation important?

The Schrödinger equation helped them to detect where the electron could be at any given moment. The significance was that electrons had extremely unpredictable behaviors, but physicist Erwin Schrödinger’s experiment tamed the situation. They realized that electrons did the same, too.

Why did Schrödinger create his equation?

His great discovery, Schrödinger’s wave equation, was made at the end of this epoch-during the first half of 1926. It came as a result of his dissatisfaction with the quantum condition in Bohr’s orbit theory and his belief that atomic spectra should really be determined by some kind of eigenvalue problem.

Is Schrödinger equation correct?

Consider the Schrödinger equation, which allows you to compute the “wave function” of an electron. Although it gives you the answer you want, the wave function doesn’t correspond to anything in the real world. It works, but no one knows why. The same can be said of the Schrödinger equation.

How do you solve the Schrodinger equation?

Solving the Schrodinger Equation Time-dependent Schrödinger equation The wave function of a particle undergoing a force F(x) is the solution to the Schrödinger equation: U(x) is the potential energy associated with the force: i!!!t “(x,t)=#!2 2m!2!x2 “(x,t)+U(x)”(x,t) F=! “U “x

Is the Schrödinger equation time dependent or position dependent?

Time-dependent Schrödinger equation: Separation of variables Since U(x) does not depend on time, solutions can be written in separableform as a part that is only position dependent and a part that is only time dependent: i! ! !t “(x,t)=# !2

What is the Schroedinger equation for time independent probability density?

EE 439 time-independent Schroedinger equation – 7. (x,t)= (x)exp(i!t) Probability density. 3([, W)= ([, W) ([, W) = ([) H+LW ([) HLW. =[ ([) ([)] H+LWHLW. = ([) ([) The probability density is independent of time, even though the wave function itself is not.

What is the Schrodinger equation for the Hamiltonian?

The operation of the Hamiltonian on the wavefunction is the Schrodinger equation. Solutions exist for the time-independent Schrodinger equation only for certain values of energy, and these values are called “eigenvalues” of energy.