The Self cannot be ‘known’ in any objective sense because it is the ultimate subject – there is no other subject that could know it. This is why science can never tell us anything about the Self. Science works by collecting data and analyzing it; formulating theories and then using them to predict what will happen when data are gathered in a different situation. This can never be applied to Self/brahman, because brahman has no data.
Strictly speaking, vichAra refers to investigation into ‘things’ so that Atma vichAra is effectively a contradiction in terms; the Self is not a thing. Spiritual investigation has to be done rather differently. The correct term is shAstra mImAMsA and it is really scriptural ‘investigation’ that we must conduct in order to find out about the Self. Monier-Williams translates mImAMsA as “profound thought or reflection or consideration; investigation, examination, discussion”. The philosophical branch that studies the Upanishads etc at the end of the Vedas (Vedanta) is called uttara mImAMsA. (uttara means “later, following, subsequent, concluding” but also “superior, chief, excellent, dominant”.)
We ‘discover’ the Self by removing ignorance. If someone holds up a screen in front of our face and then brings an object to show us, but keeps it behind the screen, we can say nothing at all about the object. However, as soon as the screen is taken away, the object is revealed to our senses and the perception takes place automatically. Similarly, knowledge of the Self is obscured by ignorance but as soon as that ignorance is removed, the Self is immediately self-evident; we do not have to do anything to ‘investigate’ it.
Scripture functions like a mirror. When we look into a mirror, we do not literally see our face and body, we only see an image of it. Yet this enables us directly to perform whatever actions are required on the body itself – combing the hair, shaving and so on. We do not shave the image but the actual hair on the face. Similarly, the scriptures do not directly represent the Self but the information therein, when explained by a qualified teacher, directly enables the ignorance in our mind to be removed, revealing the Self-knowledge which is as though hidden beneath.
Actions will never bring about Self-knowledge, since action is not opposed to ignorance. Nor will practices such as meditation or prayer. As Swami Paramarthananda puts it, meditation will only bring about quiet ignorance.
As Shankara puts it (if he was the author of vivekachUDAmaNi v.13): “It is through reflection over the words of a truly benevolent soul that one comes to a knowledge of reality, and not through bathing at sacred places, charity or hundreds of breathing practices”.  I.e. it is through shravaNa, manana and nididhyAsana and not through asking ‘Who am I?’ that one gains Self-knowledge.
 The Crest Jewel of Wisdom; viveka-chUDAmaNi, commentary by Hari Prasad Shastri, Shanti Sadan, 1997. ISBN 0-85421-047-0.