It is an experimental result that you can find the particles in those "forbidden" regions with some probability.LagrangeEuler said:How we know that in case of finite potential well that particle is in the region where ##V>E##.
Do you want a good position or a good energy measurement? Those will lead to different results.How we know what is energy of the particle in moment when we localize it in the region with potential ##V##.
mfb said:It is an experimental result that you can find the particles in those "forbidden" regions with some probability.
You can use quantum mechanics to calculate that probability.
Do you want a good position or a good energy measurement? Those will lead to different results.
That does not exist. The particle has a unique [expectation value of the] energy, which does not depend on the position.LagrangeEuler said:That is not my question. I asked how we know energy of the particles in different region?
Measure the energy of the particle ;). Or just see if it stays in the well (and in its direct vicinity) - if it does, it is not free, otherwise it is free.http://en.wikipedia.org/wiki/Finite_potential_well
"There are two possible families of solutions, depending on whether E is less than (the particle is bound in the potential) or E is greater than (the particle is free)."
How we know from measurement is it particle free or not?
In more than 1 dimension, some potential wells are so shallow that they do not have bound states. In 1 dimension, you always have a bound state.Why I don't have it always.
Quantum mechanics is a branch of physics that studies the behavior of particles at the microscopic level, such as atoms and subatomic particles. It is based on the principle that particles can exist in multiple states simultaneously, known as superposition, and can also exhibit wave-like behavior.
Quantum mechanics is important because it helps us understand and explain many phenomena at the microscopic level that classical physics cannot. It is also the foundation for many modern technologies, such as transistors and lasers, and has significant applications in fields like cryptography and quantum computing.
Some key concepts in quantum mechanics include superposition, wave-particle duality, uncertainty principle, and entanglement. Superposition refers to the idea that particles can exist in multiple states simultaneously. Wave-particle duality refers to the dual nature of particles, which can exhibit both wave-like and particle-like behavior. The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. Entanglement is a phenomenon where two particles become connected in such a way that the state of one particle affects the state of the other, even when they are physically separated.
Quantum mechanics differs from classical mechanics in several ways. Firstly, quantum mechanics deals with objects at the microscopic level, while classical mechanics deals with objects at the macroscopic level. Additionally, classical mechanics assumes that particles have definite positions and velocities, while quantum mechanics allows for particles to exist in multiple states simultaneously. Classical mechanics also follows deterministic laws, whereas quantum mechanics involves probabilities and uncertainties.
Despite many advances in quantum mechanics, there are still several challenges in fully understanding and applying its principles. One major challenge is the development of a unified theory that can reconcile quantum mechanics with general relativity, which is necessary for a complete understanding of the universe. Other challenges include the interpretation of quantum mechanics, the role of consciousness in the measurement process, and the development of practical quantum technologies.