# Solving Difficult Wave Function Problems

• blaster
In summary, the conversation is about difficulty with expressing a cos x + b sin x in different forms and determining the quadrant for the expressions. The person is able to work out the expressions in the form k cos(x-a), but struggles with other forms such as k cos(x+a), k sin(x-a), and k(sin x+a). They are looking for help and clarification on how to approach the problem.
blaster
i am having difficulty with the wave function.
for example in the exercise we are told to write the expression :

a cos x+ b sin x in the form k cos(x-a)

This i had little problem with and was able to work out what quadrant i shoul use etc what i mean is the

all positive. sin positive, tan positive and cosine positive qudarants

but the next exercise was expressing

a cos x + b sin x in other forms such as:

k cos(x+a) k sin(x-a) and k(sin x+a)

with these i am able to work out the k. however when it comes down to the quadrat i do not no whether to take away 180 add 180 or take away 360 if you know what i mean.

Why no help?

Have I not been clear enough? Why am I not getting any help? Any questions?

$$a=A\cos\alpha$$

$$b=A\sin\alpha$$

Therefore

$$a\cos x+b\sin x=A\cos(x-\alpha)$$

Daniel.

If you've already written it in the form k cos (x-a), then you can get the others simply by doing simple arithmetic, or applying basic facts about the trig functions...

Or, isn't it possible to do the same type of work to arrive at that form from scratch? ...

try using a trig identity to go backwards, i.e. write k*sin(x-a) as a sum or difference of sines and cosines. then equate the coefficients to derive expressions for k and a.

## What is a wave function?

A wave function is a mathematical description of the state of a quantum mechanical system. It contains information about the position, momentum, and other properties of the system.

## Why are some wave function problems considered difficult?

Some wave function problems can be considered difficult because they involve complex mathematical calculations and may require advanced knowledge of quantum mechanics. They may also involve systems with multiple particles or interactions, making them more challenging to solve.

## What techniques can be used to solve difficult wave function problems?

Some techniques that can be used to solve difficult wave function problems include the variational method, perturbation theory, and numerical methods such as Monte Carlo simulations. Each method has its own advantages and limitations, and the choice of technique may depend on the specific problem being studied.

## How can symmetries be helpful in solving wave function problems?

Symmetries can often simplify wave function problems by reducing the number of variables that need to be considered. For example, if a system has spherical symmetry, the wave function can be expressed in terms of spherical coordinates, making the problem easier to solve.

## What are some real-world applications of solving difficult wave function problems?

Solving difficult wave function problems is crucial in understanding the behavior of atoms, molecules, and materials at the quantum level. This knowledge is essential in fields such as chemistry, materials science, and quantum computing. It also has practical applications in developing new technologies, such as designing more efficient solar cells or developing better drugs through computational chemistry.

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