# Sudden Perturbation Approximation Question

• jsc314159
In summary, the conversation discusses using the sudden perturbation approximation to determine the probability of an electron initially in the 1s state of H3 ending up in the |n=16,l=3,m=0> state of He3+. The answer is found to be 0 by integrating the wavefunctions in spherical coordinates and interpreting the zero result as the particle having no angular momentum in the s state. The sudden approximation assumes that the transition was quick enough for the electron's orbital angular momentum to remain unchanged.
jsc314159

## Homework Statement

In a beta decay H3 -> He3+, use the sudden perturbation approximation to determine the probability of that an electron initially in the 1s state of H3 will end up in the |n=16,l=3,m=0> state of He3+

|<n'l'm'|nlm>|^2

## The Attempt at a Solution

I actually know the answer to this but I am not clear as to why and I am wondering if there is an easier way to determine the solution.

The answer comes out to be 0. When integrating the wavefunctions |n'l'm'> and |nlm> in spherical coordinates to calculate the inner product (i.e. the probability amplitude), the integral over $$d\theta$$ returns 0. Is there an easier way to see this other than going through the calculations?

How is this result interpreted?

Thanks,

jsc

jsc314159 said:

## Homework Statement

In a beta decay H3 -> He3+, use the sudden perturbation approximation to determine the probability of that an electron initially in the 1s state of H3 will end up in the |n=16,l=3,m=0> state of He3+

|<n'l'm'|nlm>|^2

## The Attempt at a Solution

I actually know the answer to this but I am not clear as to why and I am wondering if there is an easier way to determine the solution.

The answer comes out to be 0. When integrating the wavefunctions |n'l'm'> and |nlm> in spherical coordinates to calculate the inner product (i.e. the probability amplitude), the integral over $$d\theta$$ returns 0. Is there an easier way to see this other than going through the calculations?

How is this result interpreted?

Thanks,

jsc

The spherical harmonics are orthonormal so <l' m' | l m> is zero unless l=l' and m= m'. Clearly here the result is zero since |3,0> is orthogonal to |0,0>

Physically, it simply says that a particle in an s state has no angular momentum so the probability of it being observed with l=3 is zero. The sudden approximation simply assumes that the transition was so quick that the orbital angular momentum of the electron remained unchanged.

Last edited:
Thanks nrged.

That makes it clear.

## What is the Sudden Perturbation Approximation Question?

The Sudden Perturbation Approximation Question is a theoretical model used in physics to study the behavior of a system after it has been perturbed, or disturbed, suddenly. It is often used to analyze the response of a system to a sudden change in energy or external force.

## How is the Sudden Perturbation Approximation Question used in research?

The Sudden Perturbation Approximation Question is used to simplify complex systems and make them easier to analyze. It is commonly used in quantum mechanics to study the behavior of atoms and molecules after they have been perturbed. It is also used in other fields of physics, such as condensed matter and nuclear physics.

## What are the assumptions made in the Sudden Perturbation Approximation Question?

The Sudden Perturbation Approximation Question assumes that the perturbation is sudden and short-lived, meaning that it occurs in a very short period of time compared to the overall dynamics of the system. It also assumes that the system is in a well-defined initial state before the perturbation, and that the perturbation does not significantly change the energy of the system.

## What are the limitations of the Sudden Perturbation Approximation Question?

The Sudden Perturbation Approximation Question is limited to systems that are linear and in a well-defined initial state. It also does not account for any dissipation or energy loss during the perturbation. Additionally, it may not accurately predict the behavior of a system if the perturbation is not truly sudden or if the system is highly non-linear.

## How does the Sudden Perturbation Approximation Question differ from other approximation methods?

The Sudden Perturbation Approximation Question differs from other approximation methods, such as time-dependent perturbation theory, in that it assumes the perturbation is sudden and short-lived. This allows for a simpler mathematical analysis and can often provide a good approximation for the behavior of the system. However, it may not be as accurate as other methods in certain situations.

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