Particle in Two Boxes: Impact of Dividing Barrier on Energy State

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In summary, the conversation discusses the energy of a particle in a 1-dimensional box and how it changes when the box is divided into two smaller boxes. It is found that the energy decreases when a barrier is inserted, and this is due to the restriction of the particle's freedom. This process can be simulated by a time-dependent potential and can result in a non-conserved energy due to an external energy source. The concept of entropy, as seen in Gibbs' Paradox, also relates to this idea of limiting a particle's range of freedom.
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chrisphd
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Suppose we have a particle in a 1-dimensional box, such that the particle is in its lowest energy state. The energy of a particle in a 1-dimensional box is E = h^2*n^2/(8*m*L^2). Therefore, if the particle is in its lowest energy level, n = 1, and the box has a length of d, then E = h^2/(8*m*d^2). Now suppose we divide the box into two boxes, A and B, using an impenetratable barrier so that each new box has a length of d/2. Now, if the particle is found to be in box A, the minimum energy it can have is n = 1, where E = h^2*n^2/(8*m*L^2) and therefore, E= h^2/(8*m*(d/2)^2) = 4*h^2/(8*m*d^2). This is the same for the particle being found in box B by symmetry. How is it possible that the energy has increased by simply adding a dividing barrier.
 
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  • #2
The process of insertion of the barrier would require energy. That energy would be transmitted to the particle. The whole process can be simulated by a time-dependent potential. It is known that a time-dependent potential corresponds to a non-conserved energy due to an external energy source.
 
  • #3
To Me

Well Gentleman To Me The Energy Of Particle Is Decreased On Applying Barrier,bcoz We Have Restricted Particle To Finite Area.if We Further Introduce Separation,then Again Energy Is Decreased.so What We Are Doing,is Just Limiting Its Range Of Freeness.
Have You Studied Gibb's Paradox,it Also Tell The Same Thing But Regarding Entropy.
 

1. What is the "Particle in Two Boxes" experiment?

The "Particle in Two Boxes" experiment involves a particle that is confined to two separate boxes, with a dividing barrier in between. This experiment is used to study the impact of the dividing barrier on the energy state of the particle.

2. How does the dividing barrier affect the energy state of the particle?

The dividing barrier in the "Particle in Two Boxes" experiment can either increase or decrease the energy state of the particle, depending on its placement and the energy levels of the two boxes. If the barrier is placed in between two boxes with different energy levels, it can act as a potential barrier, increasing the energy state of the particle. However, if the two boxes have the same energy levels, the barrier can act as a potential well, decreasing the energy state of the particle.

3. What factors influence the impact of the dividing barrier on the energy state of the particle?

The impact of the dividing barrier on the energy state of the particle is influenced by several factors, including the size and shape of the boxes, the position and height of the barrier, and the energy levels of the two boxes. These factors can all be adjusted in the experiment to observe their effects on the particle's energy state.

4. What is the significance of studying the "Particle in Two Boxes" experiment?

The "Particle in Two Boxes" experiment has significant implications in the field of quantum mechanics. It helps us understand the behavior of particles in confined spaces and the impact of barriers on their energy states. This experiment also has applications in technology, such as in the development of quantum computers and nanotechnology.

5. Are there any real-world applications of the "Particle in Two Boxes" experiment?

Yes, the "Particle in Two Boxes" experiment has several real-world applications. It is used in the development of quantum technologies, such as quantum computers, where particles are confined to small spaces and barriers are used to manipulate their energy states. This experiment also has applications in the study of materials at the nanoscale, as well as in understanding the behavior of particles in confined spaces, such as in nuclear reactors.

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