Quantum mechanics is concerned with the problem of finding the probability of the wave function

It can be seen directly that it is like this, rnl is the radial wave function, ylm is the spherical harmonic function, its subscript is meaningful, and rnl is the principal quantum number is n, angular momentum.

In the case of l, the spherical harmonic function ylm represents the case where the angular quantum number is l and the z component is m, and the coefficients before r represent the probability amplitude of this state.

Squaring the probability amplitude gives its probability.

Therefore, the probability of r21y10 is (1 2) 2=1 4, and the probability of the next state r21y1-1 is 3 4.

In summary, the principal quantum number can be brought to the equation to find the hydrogen atom energy as, and the probability is 100%.

The square of angular momentum is l(l+1)h2=2h2 (is h, there is a horizontal line, the same is below).

The angular momentum z-component is mh=0 or -h, and its probability distributions are 1 4 and 3 4, respectively.

The average value of the mechanical quantities.

It is to multiply the probability by its eigenvalue.

The result obtained, energy and angular momentum are the same as their quantum numbers, so it is the answer obtained earlier, the angular momentum z component is: 1 4 0 + 3 4 (-h) = -3 4h. That's it

To put it simply, aren't there two nlms, 210, and 21-1, and the preceding constant c is the probability amplitude.

The probability of a state is |c|^2

1. Wave function hypothesis: The state of a microscopic physical system is fully described by a wave function.

2. Quantum state evolution hypothesis: The evolution of the state of a quantum system over time satisfies the Schrödingham's equation.

3. Operator assumption: Observable measurements in quantum mechanics are represented by Hermitian operators.

4. Measurement assumption: If the operator f is a mechanical quantity in quantum mechanics, its orthogonal normalized eigenletter sail attack number.

5. Particle homogeneity assumption: In a quantum system, there are particles with identical properties, and the exchange of any two such particles will not change the state of the system.

The wave function is a function that describes the behavior of matter in the microscopic scale, ** double-slit interference experiment of electrons, the previous content, the experiment is the original code of quantum mechanics, because it reveals the wave nature of electrons, in order to describe this non-particle behavior, scientists have introduced macroscopic physical waves, water waves and other mechanical waves, the cosine concept cosine (x), but electrons have a body and cannot loom in space, nor should they prefer any position x, so the movement of free electrons does not conform to this mathematical form, Therefore, Born proposed the probabilistic wave interpretation, arguing that the wave function represents the possibility of the particle's position, rather than describing the trajectory of the particlee，ix|，|cosx，isinx|, 1, means that the probability of free particles moving in space is equal everywhere, and there will be no fluctuations, which follows the principle of physical reality.

The wave function is a function that changes over time and is the mathematical representation of all electromagnetic waves.

The wave function is a complex function used to characterize the state of microscopic particles.

If we want to understand the theory of probability, we have to talk about another theory, determinism.

If we are playing billiards now, according to determinism, the moment you putt and hit the ball, the trajectory of the ball is determined, which is in accordance with the laws observed by classical mechanics.

However, the theory of probability is that the moment you putt and hit the ball, even if you put the ball with the same force or something, it will produce different results. The ball may roll in all directions, which is in line with quantum mechanics.

However, the Royal Academy of England once issued a letter of apology, in which it was written that people used to worship the classical mechanics of Newton and others, and had always followed determinism.

However, quantum mechanics shows that everything in the world is composed of ultra-small particles, and every situation is determined by the quantum wave function, that is to say, it is a probability that no one knows exactly what it is, so probability theory finally overwhelmed determinism in the twentieth century, and since then, determinism has withdrawn from the stage of history.