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Qmechanic ♦
Qmechanic ♦
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In Bohmian mechanics, the term $$\begin{equation} Q = -\frac{\hbar^2}{2m}\frac{\nabla^2 R}{R} \end{equation}$$

is regarded as the quantum potential term. However this is merely a term from the real part of the quantum kinetic energy equation. $$\begin{equation} T = -\frac{\hbar^2}{2m}\frac{\nabla^2 \Psi}{\Psi} \end{equation}$$

I completely fail to see why this should be regarded as anything except kinetic energy. Can someone explain?

(Yes, I know about dividing by complex quantities. When you plug in the polar form of $\Psi$ the exponentials cancel and you're left with just R$R$ so dealing with the $\Psi*$ is unnecessary.)

In Bohmian mechanics, the term $$\begin{equation} Q = -\frac{\hbar^2}{2m}\frac{\nabla^2 R}{R} \end{equation}$$

is regarded as the quantum potential term. However this is merely a term from the real part of the quantum kinetic energy equation. $$\begin{equation} T = -\frac{\hbar^2}{2m}\frac{\nabla^2 \Psi}{\Psi} \end{equation}$$

I completely fail to see why this should be regarded as anything except kinetic energy. Can someone explain?

(Yes, I know about dividing by complex quantities. When you plug in the polar form of $\Psi$ the exponentials cancel and you're left with just R so dealing with the $\Psi*$ is unnecessary.)

In Bohmian mechanics, the term $$\begin{equation} Q = -\frac{\hbar^2}{2m}\frac{\nabla^2 R}{R} \end{equation}$$

is regarded as the quantum potential term. However this is merely a term from the real part of the quantum kinetic energy equation. $$\begin{equation} T = -\frac{\hbar^2}{2m}\frac{\nabla^2 \Psi}{\Psi} \end{equation}$$

I completely fail to see why this should be regarded as anything except kinetic energy. Can someone explain?

(Yes, I know about dividing by complex quantities. When you plug in the polar form of $\Psi$ the exponentials cancel and you're left with just $R$ so dealing with the $\Psi*$ is unnecessary.)

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EvilDave
EvilDave
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Why is the Bohm quantum potential considered a potential?

In Bohmian mechanics, the term $$\begin{equation} Q = -\frac{\hbar^2}{2m}\frac{\nabla^2 R}{R} \end{equation}$$

is regarded as the quantum potential term. However this is merely a term from the real part of the quantum kinetic energy equation. $$\begin{equation} T = -\frac{\hbar^2}{2m}\frac{\nabla^2 \Psi}{\Psi} \end{equation}$$

I completely fail to see why this should be regarded as anything except kinetic energy. Can someone explain?

(Yes, I know about dividing by complex quantities. When you plug in the polar form of $\Psi$ the exponentials cancel and you're left with just R so dealing with the $\Psi*$ is unnecessary.)