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spaghetti3451
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Square potentials (finite or infinte, well or barrier) are used in intro Quantum Mechanics courses. My question is:
What does the word 'square' signify?
What does the word 'square' signify?
failexam said:My other question:
In the infinite square potential well model, the wavefunction outside the well is zero. Two reasons are usually put forward:
1. V is infinite. So Vu is infinite unless u = 0. (I don't understand what's still wrong with Vu being infinite.)
2. The particle can't be in a region of infinite potential if it lacks infinite energy. (Why not? Why should classical principles dictate quantum rules? Moreover, in the finite square well model, there is a finite probability of the particle being within the potential barrier? Isn't that a violation of the classical principle we are using in the above argument?) Therefore, u = 0.
Thanks for any help.
Rap said:Square refers to the appearance of the plot of V versus x.
Rap said:Energy is conserved in both classical mechanics and quantum mechanics. Assuming that the particle inside the well has finite energy, and the potential outside the well is infinite, then when the particle is outside the well, it will have infinite energy, which will violate the conservation of energy.
Rap said:Vu represents the potential energy of a particle outside the well. The other term in the Schroedinger equation represents the kinetic energy. Assuming that the total energy is finite and positive, if Vu were infinite, the kinetic energy would have to be negative infinity (steady state), which is impossible.
failexam said:Moreover, in the finite square well model, there is a finite probability of the particle being within the potential barrier? Isn't that a violation of the classical principle we are using in the above argument?)
How does the particle get the extra energy to jump into a potential barrier. Isn't that in violation of the principle of conservation of energy?
failexam said:There is nothing of the plot of V versus x that reminds me of a square, actually!
failexam said:There is nothing of the plot of V versus x that reminds me of a square, actually!
failexam said:But isn't that exactly what happens in quantum tunneling? How does the particle get the extra energy to jump into a potential barrier. Isn't that in violation of the principle of conservation of energy?
A better way to say it is that they are the potential energy and kinetic energy terms in the Schroedinger equation.failexam said:Howcome Vu is potential energy? I thought V was?
How can the other term represent the kinetic energy?
Its a limiting process. For example, as n grows larger, (n+1)^2- (n^2+2n) equals 1. Each term on the left grows larger without bound.failexam said:How can positive and negative infinity add to give a finite positive number?
It means no change in time.failexam said:What does 'steady state mean'?
The 'square' in quantum mechanics potentials refers to the mathematical operation of taking the square of a number. In quantum mechanics, this operation is used to calculate the probability of finding a particle in a particular position or state.
The square function is used in the Schrödinger equation, which is a fundamental equation in quantum mechanics. It is used to calculate the time evolution of a quantum system, including the probability of finding a particle in a certain state.
The square function has a physical interpretation as it represents the square of the wave function, which describes the behavior of a quantum system. The square of the wave function gives the probability of finding a particle in a certain state or position.
The square function plays a crucial role in determining the behavior of particles in quantum mechanics potentials. It is used to calculate the probability of finding a particle in a particular state, which ultimately determines its behavior and interactions with other particles.
Yes, the significance of 'square' in quantum mechanics potentials can be explained visually through the wave function, which is often represented as a graph. The square of the wave function is represented by the area under the curve, which gives the probability of finding a particle in a particular state or position.