Tunneling through a PE barrier

In summary, the conversation highlights the concept of tunneling in Intro Physics and the confusion surrounding the violation of energy conservation. It is explained that energy conservation is not actually violated, but the kinetic energy in quantum mechanics is negative, which may be difficult to grasp. The conversation ends with a suggestion to read an introductory text on quantum mechanics for a better understanding.
  • #1
kalery
19
0
I'm still in Intro Physics, and I'm a little perplexed by the concept of tunneling. An alpha particle escapes the nucleus by overcoming a potential energy barrier created by Coulombic repulsion with the protons of the nucleus, but this is a spontaneous process and does not require E input, according to my textbook. Energy conservation is violated to allow the alpha particle to move through this E barrier for a brief time interval because unk(E)unk(t) >= hbar. What's going on here... I mean, is this really what happens... How can energy conservation be violated? I thought that despite all the quantum phenomena violating classical Newtonian physics, that energy conservation still is supposed to remain constant?
 
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  • #2
Conservation of energy is not violated. What you think is kinetic energy, namely the classical kinetic energy of a point particle as it travels through the barrier, seems to be negative, i.e., [tex]K = E-U(x)[/tex]. The total energy, namely [tex]E[/tex], remains constant, and so conserved.

So now you just need to come to grips with the fact that the kinetic energy is negative. In quantum mechanics, the kinetic energy is an operator acting on a wavefunction, and in 1D is given by [itex]-\hbar^2 \frac{d}{dx}[/itex]. If the kinetic energy is negative, it means that the wavefunction is a growing or (usually) decaying, instead of oscillating. Think of this operator acting on [tex]\psi(x) = e^{-\lambda x}[/tex], versus [tex]\psi(x) = e^{i k x}[/tex].
 
  • #3
dont understand what is Ibrits talking about... too complex -.-"
What do you mean by kinetic energy is an operator acting on a wavefunction" and "wavefunction is a growing or (usually) decaying, instead of oscillating"?
 
  • #4
kensaurus: Read an introductory text on quantum mechanics.
 

1. What is tunneling through a PE barrier?

Tunneling through a PE (potential energy) barrier is a phenomenon in quantum mechanics where a particle with less energy than the barrier can pass through it due to wave-like properties.

2. How does tunneling through a PE barrier work?

Tunneling through a PE barrier occurs because of the uncertainty principle, which states that the position and momentum of a particle cannot be known simultaneously. This allows for the particle to have a small probability of appearing on the other side of the barrier.

3. What factors affect the probability of tunneling through a PE barrier?

The probability of tunneling through a PE barrier is affected by the width and height of the barrier, as well as the energy and mass of the particle. A wider or taller barrier, as well as a heavier or lower energy particle, will decrease the probability of tunneling.

4. What are some real-world applications of tunneling through a PE barrier?

Tunneling through a PE barrier has many applications in various fields, such as nuclear physics, semiconductor devices, and scanning tunneling microscopy. It is also a crucial phenomenon in the development of quantum computing.

5. Are there any limitations to tunneling through a PE barrier?

While tunneling through a PE barrier is a well-established phenomenon in quantum mechanics, it is limited by the uncertainty principle and the size of the barrier. Extremely high or wide barriers may not allow for significant tunneling to occur. Additionally, the phenomenon is not applicable to macroscopic objects due to their large mass and energy.

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