Based on the web page context and the search results, here is a possible in-depth analysis of the meeting between the author and Julie on March 18, 1996, using psychological terms and meaning:

• The meeting between the author and Julie can be seen as an attempt at reconciliation, which is a process that’s focused on healing relationships1. Reconciliation involves acknowledging hurtful actions and their resulting emotions, apologizing for one’s part in an issue, forgiving and letting go of the associated grudges1.
• The author initiated the reconciliation process by seeking out Julie at her college, where he had not seen her for over three years. He wanted to somehow make amends for his past wrongs and regrets, which had haunted him since their breakup. He also wanted to see her before she got married to someone else, which he learned from a mutual friend.
• Julie was initially surprised and suspicious of the author’s visit, but she agreed to talk to him and go for a walk with him. She was curious about his motives and his life, but also cautious about reopening old wounds. She had moved on from their relationship and was happy with her fiancé, Brian.
• The author and Julie had a long and honest conversation, where they shared their memories, feelings, and experiences. They also played piano for each other, which was something they used to do when they were dating. They reconnected on an emotional level, but also maintained a respectful distance.
• The author expressed his sincere apology for cheating on Julie and hurting her in the past. He looked into her eyes and asked for her forgiveness. He also wished her well in her marriage and career. Julie accepted his apology and forgave him. She also asked for a letter that he had written to her after their breakup, which she had never received. She wanted to have it as a souvenir of their relationship.
• The author and Julie parted ways with a handshake, which turned into a hug. They both felt a sense of closure and peace. They realized that their reunion was the final chapter of their story, which had begun and ended on the same date: March 18th. They also realized that they still had good memories of each other, which they could cherish without bitterness or resentment.
• The meeting between the author and Julie can be seen as a successful reconciliation process, which resulted in an improvement in their relations and a reduction of their injustice gap2. They were able to deal with the emotional, epistemic, and material legacy of their past3, and restore some trust and respect between them. They were also able to let go of their grudge and move on with their lives.