Solving for DeltaX in a Quantum Well: Uncertainty Principle and Energy Analysis

In summary, the problem is about a quantum well with a width of DeltaX and a depth of 1.0 eV, where an electron has a potential energy of -1.0 eV inside the well and 0 eV outside. The task is to use the uncertainty principle to find the value of DeltaX where the total energy (kinetic and potential) of the electron in the well is zero. The student attempted to solve for DeltaX by setting the total energy to 0, but doubts the accuracy of their answer. They also mention that the mass of the electron was not given in the exam. They are requesting help from others to solve the problem.
  • #1
D__grant
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Homework Statement



-This is a problem on my practice final that I haven't been able to solve. Hoping someone out there can take a crack & clarify it for me.

Quantum wells are devices which can be used to trap electrons in semiconductors. If the electron is in the well it has a lower energy than if it is outside, so it tends to stay in the well. Suppose we have a quantum well which has a width of DeltaX and a depth of 1.0 eV , i.e. if the electron is in the well it has a potential energy of -1.0 eV and if it is outside it has a potential energy of 0 eV. Use the uncertainty principle to find the value of DeltaX for which total energy kinetic & potential of an electron in the well is zero.
Note: This is the smallest size well we can have because if deltaX is any smaller, the total energy of the electron in the well will be bigger than zero, and escape.



Homework Equations


1. E=KE+PE
2. Vo= -1 eV
3. Total Energy > 1/2m x (h/2piDeltaX)^2 - Vo

The Attempt at a Solution



I set the Total Energy=0 and attempted to solve for deltaX. My first solution was the the order of 10^-11 but I doubt I answered it correctly. Also, the mass of an electron was not given on the exam so I'm wondering if there's a different path to take. Thank you
 
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  • #2
Anyone care to take a shot at this? I'm desperate for help & I'm not sure why no one's attempted it. I read the stickies & tried following the forum's conventions as best I could...

thank you all
 

FAQ: Solving for DeltaX in a Quantum Well: Uncertainty Principle and Energy Analysis

What is the uncertainty principle and how does it relate to solving for DeltaX in a quantum well?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle at the same time. When solving for DeltaX in a quantum well, this principle is important to consider because it affects the precision and accuracy of the calculated value.

Why is solving for DeltaX in a quantum well important in quantum mechanics?

Solving for DeltaX in a quantum well allows scientists to determine the range of possible positions for a particle within a confined space. This is crucial in understanding and predicting the behavior of particles at the quantum level, which is essential in many areas of modern science and technology.

What factors influence the value of DeltaX in a quantum well?

The value of DeltaX in a quantum well is influenced by several factors, including the mass of the particle, the size and shape of the well, and the potential energy within the well. Additionally, the uncertainty principle also plays a role in determining the value of DeltaX.

How does energy analysis play a role in solving for DeltaX in a quantum well?

Energy analysis is an important tool in solving for DeltaX in a quantum well. By analyzing the energy levels of the particle within the well, scientists can determine the range of possible positions and therefore the value of DeltaX. This provides a more comprehensive understanding of the quantum system being studied.

What are some real-world applications of solving for DeltaX in a quantum well?

Solving for DeltaX in a quantum well has many practical applications, including in the development of quantum computing, nanotechnology, and quantum sensors. It also has implications in fields such as chemistry, materials science, and medicine, where understanding the behavior of particles at the quantum level is crucial.

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