Do the Particle and Associated Wave Always Move in the Same Direction?

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The discussion centers on whether a particle and its associated wave always propagate in the same direction. It is noted that the particle's movement is intrinsically linked to the movement of its wave packet. The relationship between the particle and wave is crucial for understanding quantum mechanics. Participants explore the implications of this connection for wave-particle duality. Ultimately, the consensus is that the particle's motion is directly tied to the behavior of its wave packet.
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Do the particle and the associated wave move (propagate) along the same
direction?
 
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? The only movement of the particle is the movement of its wave packet.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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