#### Write4U

**Valued Senior Member**

No, I don't. I believe you are parsing this incorrectly. The "Pilot wave" acts in accordance with Schrodinger, the particle's "guiding equation" pertains to the particle's physical properties, such as speed and position. The total is an augmentation of the Schrodinger Equation .Do you now agree with me that Bohm's pilot waves (described by his "guiding equation") behave very differently from the waves in Schrodinger's description of quantum mechanics?

I agree with the following:

**Collapse**

**of the universal wavefunction never occurs in de Broglie–Bohm theory. Its entire evolution is governed by Schrödinger's equation, and the particles' evolutions are governed by the guiding equation. Collapse only occurs in a phenomenological way for systems that seem to follow their own Schrödinger's equation. As this is an effective description of the system, it is a matter of choice as to what to define the experimental system to include, and this will affect when "collapse" occurs.**

### De Broglie–Bohm theory - Wikipedia

en.wikipedia.org

**The equation which gives the velocity of a particle is known as the guiding equation which can be used to calculate the trajectory of a particle.**

**This trajectory depends on the particle's starting position and the wavefunction for all times.Mar 3, 2021**

Constructing Numerical Methods For Solving The Guiding Equation In Bohmian Mechanics

2.3 Derivation of the guiding equation

Constructing Numerical Methods For Solving The Guiding Equation In Bohmian Mechanics

2.3 Derivation of the guiding equation

Hamiltonian mechanics use the Hamiltonian equations to determine motion classically and with those equations it is possible to determine the time derivative of the position. This equation has a corresponding equation in Bohmian mechanics where it is possible to derive an equation for a particle. This equation is defined differently since the wavefunction is a complex function and the fact that Schrödinger equation is a first order with respect of time. By taking that into account, the corresponded Hamiltonian equation for Bohmian mechanics gets defined somewhat differently.

**2.4 Examples of use with the guiding equation (11)**

The guiding equation can be used in known solutions to Schrödinger equation for different potentials. In the examples of an infinite wall or box, the result of using the guiding equation with the wavefunction for an eigenvalue of the energy gives a zero velocity of the particle everywhere.

This means that the particle remains at a fixed position. Using several eigenvalue solutions to create a wave packet makes a non-zero velocity when using the guiding equation. This can also be observed in the Hydrogen atom, where the ground state eigenfunction also produces a zero velocity for the electron [8,9]. The fixed position solution of the trajectories is non-classically and is a result of the quantum potential. The quantum potential and the external potential can cancel each other to give the particle a zero velocity [8,9].

**2.5 Creating a wave packet**

Fixing the position of a particle to an exact position in space in quantum mechanics means that the range of the momentum of the wavefunction is infinitely large. By creating an uncertainty in the position by creating a wider range of possible detection positions will narrow the range of momentum. This can be done by creating a wave packet which travels like a wave with an almost fixed shape. The shape will be stretched when it is traveling.

chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.diva-portal.org/smash/get/diva2:1533848/FULLTEXT01.pdfInserting particles in the wave packet means that the particles must follow this wave packet. When the wave packet later interacts with its environment in the form of a potential, the potential will affect the wave packet and thus the particles’ trajectories by the guiding equation. The particles trajectories depend on their starting position at a specific time. The velocity at that time is dependent on the wavefunction and the position of the particle in the wavefunction and thus it is not possible to choose the velocity independently of those variables [8,9].

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