Quantum Mechanical Tunneling Probability

In summary, the conversation centers around the question of what is the probability of a 2 gram object quantum mechanically tunneling through a rectangular barrier. The speaker argues that the object's mass is significantly greater than an electron and therefore the probability would be negligible. They also question the use of wave-function to describe a macroscopic object. The other person suggests that the professor may have wanted a numerical answer and brings up the limitation of treating a 2 gram object as a point particle.
  • #1
Demon117
165
1
I recently took an exam in which the professor asked the following question:

Suppose an object of mass 2 grams were incident on a rectangular barrier of height 20 cm and width 2.0 cm. What is the probability that the object will quantum mechanically tunnel and appear on the other side?

I argued that since this object has a mass on the order of 10^27 times greater than the electron that qualitatively the probability would be negligible. Furthermore I argued that such a macroscopic object could be described classically so why would we describe such an object by a wave-function propagating in space? I'd like to hear your ideas on the matter and see what others say. Thanks!
 
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  • #2
I'd say that you're right, it's "negligible", but your professor probably wanted you to come up with a number. You have to play to the audience. :smile:

I'd also say that Schrodinger quantum mechanics is intended to describe a point particle, and treating a 2 gram object as if it were a point particle is pretty hokey. What if half the object penetrated the barrier and the other half did not?
 

1. What is quantum mechanical tunneling probability?

Quantum mechanical tunneling probability refers to the likelihood of a quantum particle passing through a potential energy barrier. It is based on the principles of quantum mechanics and describes the probabilistic nature of particles at the quantum level.

2. How is quantum mechanical tunneling probability calculated?

The calculation of quantum mechanical tunneling probability involves using the Schrödinger equation to determine the wave function of the particle and then applying boundary conditions to solve for the probability of the particle passing through the barrier.

3. What factors affect quantum mechanical tunneling probability?

The primary factors that affect quantum mechanical tunneling probability are the width and height of the potential energy barrier, as well as the energy of the particle. Additionally, the particle's mass and the shape of the potential energy barrier can also play a role.

4. Can quantum mechanical tunneling probability be observed in real-world situations?

Yes, quantum mechanical tunneling probability has been observed in various physical systems, such as in electron tunneling in semiconductor devices and in alpha decay of radioactive nuclei. It is a fundamental concept in quantum physics and has practical applications in technological advancements.

5. How does quantum mechanical tunneling probability relate to the uncertainty principle?

Quantum mechanical tunneling probability is closely related to the uncertainty principle, which states that the position and momentum of a particle cannot be simultaneously known with absolute certainty. The probabilistic nature of particles at the quantum level, including the probability of tunneling through a barrier, is a manifestation of this principle.

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