Arithmetic Question Involving Quantum Physics

In summary, the conversation discussed the calculation of the length of a one-dimensional box based on the allowed energies of an electron. The equation E_n=\frac{h^2n^2}{8mL^2} was given, and the individual attempted to solve for L using \Delta E_n=\frac{h^2\Delta n^2}{8mL^2}. However, this technique did not work due to the fact that \Delta n^2 is not a constant and depends on n. This led to an incorrect answer and the individual was advised to use the correct method.
  • #1
Coop
40
0

Homework Statement



Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is the length of the box?

Homework Equations



[tex]E_n=\frac{h^2n^2}{8mL^2}[/tex]

The Attempt at a Solution



My question is, since E_n and n^2 are both on separate sides of the equation in the numerator, why can't I put Delta in front of each of these variables and solve for L?

[tex]\Delta E_n=\frac{h^2\Delta n^2}{8mL^2}[/tex] and since the energy levels are adjacent, [tex]\Delta n^2=1[/tex]

I tried doing this, but it gave me the incorrect answer. I know how I am supposed to do the problem now, I am just wondering why my original technique does not work.

Thanks,
Cooper
 
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  • #2
Delta is shorthand for small change; essentially a derivative.
when you change n^2 to (n+1)^2 , it is not really a small change,
and clearly the change in the second depends on n.
(that is, 1^2 is 1, but 2^2 = 4 ... a difference of 3
5^2 = 25 , but 6^2 = 36 ... a difference of 11 , which is 3½ times as much.
 

FAQ: Arithmetic Question Involving Quantum Physics

What is the connection between arithmetic and quantum physics?

The connection between arithmetic and quantum physics is that arithmetic is a fundamental tool used in the mathematical equations and calculations of quantum physics. Without arithmetic, we would not be able to accurately describe or understand the behavior of particles at the quantum level.

How does quantum physics affect arithmetic problems?

Quantum physics affects arithmetic problems by introducing new principles and rules that must be followed when dealing with particles and their interactions at the quantum level. For example, in quantum physics, numbers can have both real and imaginary components, which can greatly impact arithmetic calculations.

Can quantum computers solve arithmetic problems faster than classical computers?

Yes, quantum computers have the potential to solve certain arithmetic problems much faster than classical computers. This is because they use quantum bits, or qubits, which can exist in multiple states at once, allowing for parallel processing and faster calculations.

What is the role of quantum mechanics in solving arithmetic problems?

Quantum mechanics plays a crucial role in solving arithmetic problems because it provides the mathematical framework and principles for understanding and predicting the behavior of particles at the quantum level. Without quantum mechanics, we would not have the tools or understanding to accurately solve complex arithmetic problems involving quantum physics.

Is quantum arithmetic different from traditional arithmetic?

Yes, quantum arithmetic is different from traditional arithmetic in that it follows the principles and rules of quantum mechanics, which can result in different outcomes and solutions. For example, in traditional arithmetic, we are used to numbers having a single value, while in quantum arithmetic, numbers can have multiple values and states simultaneously.

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