Half-life using Schrodinger's wave equation

In summary, the conversation discusses estimating half life using Schrodinger's time-independent wave equation and dividing the energy barrier into smaller segments. The equation for the probability of tunneling is mentioned and the idea of using calculus to arrive at better approximations is proposed. However, the individual's attempt at solving the integral did not yield meaningful results and they are seeking help.
  • #1
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Hello guys!

I've been learning how to estimate half life using Schrodinger's time-independent wave equation. In class, we divided the energy barrier into five smaller segments just like this webpage http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/alpdet.html#c1

I was wondering if we could divide the barrier into a large number of segments n to arrive at better approximations using calculus. In class, we used the following equation for the probability of tunneling

My work is shown below

$$ψ = e^{-βx}
\\β = \frac {\sqrt {2m_α(U - E_α)}} {ħ}
\\U = \frac {kq_1q_α} {x}
\\ψ^2 = e^{-2βx}
\\ψ_{total} = e^{-2∫β(x)dx}$$

I solved the integral and put a few numbers but didn't really get anything meaningful, so any help would be greatly appreciated
 
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  • #3
Also, I have moved this post to the homework forum.
 

1. What is Schrodinger's wave equation?

Schrodinger's wave equation is a mathematical equation used in quantum mechanics to describe the wave-like behavior of particles. It was proposed by Austrian physicist Erwin Schrodinger in 1926.

2. How does Schrodinger's wave equation relate to half-life?

Schrodinger's wave equation can be used to determine the probability of a particle decaying in a given amount of time. This probability can be used to calculate the half-life of a radioactive substance.

3. Can Schrodinger's wave equation be used to predict the exact moment of decay?

No, Schrodinger's wave equation can only predict the probability of decay within a certain time frame. It cannot determine the exact moment of decay for a specific particle.

4. How is half-life calculated using Schrodinger's wave equation?

To calculate half-life, the probability of decay for a specific time frame is set to 50%. This time frame is then equal to the half-life of the substance.

5. Are there any limitations to using Schrodinger's wave equation to calculate half-life?

Yes, Schrodinger's wave equation is based on probability and is not always accurate for predicting the decay of individual particles. It is more useful for predicting the overall behavior of a large group of particles.

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