Manifestation: It's Social, Not Quantum
The collapse of the wave function refers to the state of a particle called superposition. The state of being indeterminate between two or more possible outcomes. Schrodinger determined that the outcome is determined only when observed by a conscious observer because that's the endpoint where the information conveyed by the state of the particle has context and relevance with regard to the passage of time and of course, cause and effect.
From this concept, many people have taken it a step further to imply that if our observations have such a drastic effect upon the unfolding of reality, would it not then apply that our state of mind could have an effect upon how the future unfolds as much so as that the future unfolds? The interpretation being that our mood and sense of peace and serenity could somehow affect, at the level of the quantum realm and the level of a sub-atomic particle, the way that such state unfolds from the quantum state of superposition to classically deterministic state to become the next "Planck moment" (the smallest measurable movement of matter that constitutes a step forward in time in the classical sense). The idea that the better our state of mind then the better will be the results of the impact of our power of observation (to collapse the wave function) which yields reality itself.
Some of what I've expressed in my writing, especially within the many Butterfly Dragon chapters and stories that deal with Quantum Physics might sound a little "woo woo".
definition courtesy of Google Dictionary
In defence of new agers, I believe that what they're referring to by manifestation refers more to one's state of mind more so than affecting reality itself. It's common knowledge that our mindset alone can drastically affect the way that we deal with challenges presented to us, and that's not particularly unhealthy advice for anyone. We can survive the worst turmoil with the right attitude as much so as we can be humble in the best of circumstances. That's all attitude and something that one can reinforce within themselves to a degree. We are social creatures after all. We each depend upon a network of people to survive and therefore our attitude can be affected externally when our ideas about how society should be run come into conflict with one another.
Please allow me to clarify first before you jump to any conclusions. I've personally spoken about manifestation and likely in a way that sounds like its referring to Quantum Physics or Quantum Consciousness and that I've got my concepts mixed up somehow, which I don't and that's because I've never regarded the collapse of the wave function and the necessity for the presence of an observer to be any sign of manifestation or even my interpretation of manifestation. I mean that gets into many different possibilities which are fun to speculate but until we've proven those possibilities beyond a doubt, my mind is open to the many possibilities, but none are a definite answer. You could say that our understanding of the universe is in a state of superposition itself that will collapse into a theory that accommodates our observations.