Can a Quantum Bouncing Ball Tunnel Through an Infinite Potential Barrier?

In summary, a quantum bouncing ball is a theoretical concept in quantum mechanics where a microscopic particle bounces back and forth between two points due to its wave-like behavior. It differs from a classical bouncing ball in that it follows the laws of quantum mechanics rather than classical mechanics. Studying quantum bouncing balls helps us understand the principles of quantum mechanics and has potential applications in fields such as quantum computing. While we cannot observe a quantum bouncing ball in real life, there are systems in nature that exhibit similar behavior. These include electrons in an atom and phonons in a crystal lattice.
  • #1
supakorn
11
0
if a ball of mass m moving under the potential : V(z) = mgz for z > 0 and V(z) = [tex]\infty[/tex] for z [tex]\leq0[/tex].What is the value of T : (Transmission coefficient)?


i get : T = 0
 
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  • #2
supakorn said:
if a ball of mass m moving under the potential : V(z) = mgz for z > 0 and V(z) = [tex]\infty[/tex] for z [tex]\leq0[/tex].What is the value of T : (Transmission coefficient)?

i get : T = 0

Eh, yes, of course.
 
  • #3


The value of T in this case is indeed zero. This is because the potential V(z) is infinite for z≤0, meaning that the ball cannot pass through this point. Therefore, the transmission coefficient, which represents the probability of the ball passing through the potential barrier, is zero. This result is consistent with classical mechanics, where a ball cannot pass through an infinite potential barrier. In quantum mechanics, particles can exhibit wave-like behavior and have a non-zero probability of tunneling through potential barriers, but in this case, the potential is too high for the ball to pass through.
 

FAQ: Can a Quantum Bouncing Ball Tunnel Through an Infinite Potential Barrier?

What is a quantum bouncing ball?

A quantum bouncing ball is a theoretical concept in quantum mechanics where a microscopic particle is confined in a potential well and bounces back and forth between two points due to its wave-like behavior.

How is a quantum bouncing ball different from a classical bouncing ball?

A classical bouncing ball follows the laws of classical mechanics and can be predicted using Newton's laws of motion. However, a quantum bouncing ball follows the laws of quantum mechanics and its behavior is described by the Schrodinger equation, which takes into account the particle's wave-like nature.

What is the significance of studying quantum bouncing balls?

Studying quantum bouncing balls can help us understand the principles of quantum mechanics, which govern the behavior of particles at the microscopic level. It also has potential applications in fields such as quantum computing and information processing.

Can we observe a quantum bouncing ball in real life?

No, quantum bouncing balls are purely theoretical and cannot be observed in real life. This is because the effects of quantum mechanics are only noticeable at the microscopic level, and a quantum bouncing ball is too small to be observed by the naked eye.

Are there any real-world examples of systems that behave like quantum bouncing balls?

Yes, there are systems in nature that exhibit behavior similar to quantum bouncing balls, such as electrons in an atom and phonons (vibrations) in a crystal lattice. These systems can be described by the same mathematical principles as a quantum bouncing ball, but on a larger scale.

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