Quantum Mechanics of Little

In the 20th century, physicists should be drums: happy that the building of physics is perfect, there is no new theory of new phenomena, the rest is just tinkering, physics is perfect, and it should be sad: physicists should no longer exist to turn into engineers. Before 1900, basically traditional physics, whether it is mechanics, electromagnetics, thermodynamics, has achieved great achievements, explaining the basic phenomena that people recognize, and the people who fail to explain the problems of time rather than tools. Soon, this pessimism (say, alas, physicists are going to lose their jobs, but for all mankind should be proud, because humans seem to have understood God) was thrown away by new ideas, physicists have a job! A large part of these new phenomena is related to quantum mechanics, and then the subsequent development of quantum mechanics is the main part of modern physics: particle physics, nuclear physics, atomic physics, condensed matter physics, and so on. Previous branches of traditional physics should also be referred to as classical physics.

Quantum mechanics is a major subversion of classical physics. Classical physics believes that:

1. The world is deterministic: as long as there is enough information, the future development of a physical system can be fully predicted. Einstein said: "God does not throw dice, is a very good expression." Despite Einstein's non-recognition of the specific view of quantum mechanics, he played a big role in the early development of quantum mechanics.
2. The essence of light is the wave, and the essence of the general matter is the particle. Of course, before quantum mechanics, not everyone thought that the essence of light was a wave, such as Newton thought it was a particle, but none of them formed a system, and the essence of light was that the wave was the greatest play in Maxwell's theory of electromagnetic field.
3. The nature of the world is continuous, such as temperature, momentum is continuous change.
4. Observation can be objective, whether you observe or not, the fact that it happens is happening.

These classical assumptions seem invulnerable, but quantum mechanics challenges these assumptions one by one

1. The world is not deterministic: below the atomic scale, you can only predict probabilities, for example, you cannot determine where an electron is, but what the likelihood is.

2. Whether it is light or matter, there are wave-particle duality.

3. In certain circumstances, the physical quantity is discrete, for example, time, quality, length, there is a minimum value, below this value, people do not know what the meaning of him.

4. Observation will affect the experiment. Of course, this is the most famous is Schrödinger's cat, so a topic, it seems that everyone knows, we science and technology, arts, some people come to play handsome??。 But I prefer to agree with another formulation of the argument: "Is the moon there when nobody looks?" “

Why is quantum mechanics so different from our intuition that it can be accepted? Very simple, explaining some phenomena that cannot be explained.

Then why did quantum mechanics start? There are a few important questions to be talked about.

First, the problem of blackbody radiation

Traditionally, black objects absorb all the light without reflecting it. Obviously this is wrong: if only absorbing non-reflective, the black object temperature will always rise, the result is to wear a black clothes will be burnt. So since all objects radiate energy, how much is the radiation rate? The final logical explanation for this problem is the quantization of energy based on Planck. It is said that Planck's quantization statement is to solve the so-called "ultraviolet catastrophe", in fact, the proposed ultraviolet catastrophe in the 10 years after the Planck, so Planck just to get a more consistent with the experimental data theory.

Second, the photoelectric effect

Simply put, the light on the surface of the metal will produce electrons. The experimental observations at the time were like this.

1) The amount of electrons is related to the intensity (density) of the irradiated light; 2) The maximum energy is related to the light frequency of irradiation.

Einstein's concept of photon was established in 1905 to explain the problem. He said that light is a part of the energy of a photon is HV, where h is the Planck constant (H=6.62606896x10^ ( -34) J s), and V is the frequency. When light shines on a metal surface, electrons are activated, but an electron can only accept the energy that a photon contributes, so the natural maximum energy is only light with the frequency of the photon. The interpretation of the photoelectric effect is also an important starting point of quantum mechanics, but once quantum mechanics develops the theory that everything is a probability, Einstein no longer supports quantum mechanics after the revolution. Of course, Einstein did not reject probabilities and statistics, but did not have enough reason to do so. Einstein was most opposed to the principle of uncertainty. In other words, Einstein thought quantum mechanics was right, but not complete. This is the best history of Einstein and Bohr in a 1930 discussion, Einstein tried to use some of the ideological experiment to find a precise measurement of the two incompatible physical quantities, such as coordinates and momentum. And Bohr solved the problem of Einstein. But it was clear that Einstein was not completely convinced. But it must be said that Einstein's deep thinking of quantum mechanics goes far beyond the many people who fully supported quantum mechanics at the time.

Third, whether the matter is a wave or a particle

The light has two elephants, what about the matter particles? De Broglie that there are two of elephants in any substance. Then why, the light diffraction through a narrow slit, the person out of a door without diffraction? Very simple, although there are two of elephants, but this effect is extremely not obvious, so the particle-oriented. For example a person 60kg, movement speed 1m/s, then his wavelength =h/momentum=h/60=1.1^-35m, can ignore. If an electron (mass = 9.11 x 10¯31 kg) has a speed of 5.31 x 106/s, its wavelength is 1.37 x 10¯10 m, which is larger than the electron itself 10^6 times!

Well, I admit, the above is just think of what to say, the following is what I want to do: I am very selfish, have not done double slit interference experiment, write this is to write a program to play this double slits experiment just, only for the animation effect is more beautiful. The procedure has to start from the theory, in fact, it is very simple to solve the two-dimensional Schrodinger equation:

2. The second method is simpler and finite difference method.

This method is so simple that I am too lazy to write the process. In fact, it is written that this has been written, a little patience, simply put the program up. Note: Not Matlab is written by Scilab.

Clear;lines (0); N = 200; Grid Sizel = 4;dt = 0.0005;x = Linspace (-l,l,n); y = X;a = 2*l/(n+1); bx = 1;by = 0.025;AA = a/2;//potential function desc  Ribing the screen+slitsfunction z = V (xx,yy) z = 0;      if (ABS (XX) <L/40) Then if (ABS (YY-1) >1/2) Then if (ABS (yy+1) >1/2) then z = 200;   End End endendfunctionu = Zeros (n,n), v = U;BT = 1* (2*%PI/1),//initial wavefunctionfor i=2:n-1 for j=2:n-1 u (i,j) =    cos (bt* (x (i)) *exp (-bx* (x (i)-L/2) ^2) *exp (-by* (Y (j)) ^4);  V (i,j) =-sin (bt* (x (i)) *exp (-bx* (x (i)-L/2) ^2) *exp (-by* (Y (j)) ^4); ENDENDSC = 1/SQRT (max (u.^2+v.^2)); u = sc*u;v = SC*V;SC = 1;u = Sc*u;v = SC*V;SC = 0.5/A^2;FG = SCF (0); fg.figure_size = [88  0+18,720+134];fg.color_map = Jetcolormap (n);//time stepping loopfor k=1:2000 drawlater ();  CLF ();  Matplot (((u.^2+v.^2). ^ (1/2)) *255+1, "042");  Ax = GCA ();  Ax.tight_limits = "on";  Ax.margins = [1,1,1,1]*0.05;  Drawnow ();  Disp (sum (u.^2+v.^2));  Name = sprintf ("%04d.png", K);  printf ("%s\n", name); if (modulo (k,20)==0) then while (~isfile (name)) xs2png (0,name);        End end for Kk=1:1 to i=2:n-1 for j=2:n-1 H =-sc* (U (i+1,j) +u (i-1,j) +u (i,j+1) +u (i,j-1) -4*u (i,j));        H = h+v (x (i), Y (j)) *u (I,J);      V (i,j) = V (i,j)-h*dt;        End end for i=2:n-1 for j=2:n-1 H =-sc* (V (i+1,j) +v (i-1,j) +v (i,j+1) +v (i,j-1) -4*v (i,j));        H = h+v (x (i), Y (j)) *v (I,J);      U (i,j) = U (i,j) +h*dt; End End EndEnd

The result is this:

　　

Quantum Mechanics of Little