Friday, March 20, 2009

Quantum Tunnelling Metaphor

I very much dislike when people use quantum physics to explain…whatever they want. But I think I can get away with it here as I am using quantum tunnelling only as a metaphor.

To start off, imagine a potential barrier of width L and potential V>E. Now consider a particle described by wave mechanics that has a wavelength,
λ = 2πħ /(√2m(E-Vo)).

For E> Vo, the wavelength is real (because the square root in the expression above is positive). However, the change in potential causes an increase in wavelength and a change in wavelength means that the particle is both reflected from and transmitted across the barrier.

For E less than Vo, the wavelength in the region of the barrier (region II) is imaginary (the square root in the expression above is negative). Because the wavelength is imaginary, the wave function decreases exponentially inside the barrier. If L is large (infinite), the wave will not cross the barrier. But if L is small, the wave will resume at the other end of the barrier, although with a decreased amplitude.

In my metaphor, the wave function is the patient and the barrier is the depression (or other illness). More severe depressions will have larger barriers. Classically speaking, a particle would not be able to pass through the barrier. However, we have just seen that the seemingly impossible is possible from a different perspective. I would say the classical perspective is the way a patient views their situation through their depression.

Inside the barrier is where the therapy occurs, working in and through the depression. While in the depression, it may seem like there is no way out as the wave function decreases, especially if the barrier is large. However, both psychotherapy and pharmacotherapy can decrease the width of the barrier, decrease the length and intensity of the depression.

An when the patient does emerge on the other side, because L isn’t infinite, they may interpret the attenuated wavelength as them being less of their original self when in fact, the variations in their mood is now more stable instead of fluctuating into extreme values as it did before they passed through the barrier of depression.

Physics saves lives.

Oh, there is also an energy barrier in a game called Rune Village which keeps unwanted souls from entering the port, but to pass through that barrier all you have to do is give the guards some money.

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