I have written about this before. So please allow me to first start by repeating the following:
When it comes to the Christian faith, there is no doctrine more important than the resurrection of Jesus. Biblical faith is not simply centered in ethical and religious teachings. Instead, it is founded on the person and work of Jesus. If Jesus was not raised from the dead, we as His followers are still dead in our sins (1Cor.15:7). Explanations try to show how something happened. That is, what is the cause for something that has happened. As I have noted elsewhere, the resurrection story started very, very, early. Also, there is an excellent post on the empty tomb issue over at Wintery Knight’s blog.
Anyway, let’s take a look at what explains the resurrection appearances. First, let’s observe the list of appearances:
• Jesus appears to Mary Magdalene, shortly after his resurrection (Mark 16:9; John 20:11-18)
• Jesus appears to the women returning from the empty tomb (Matthew 28:8-10)
• Jesus appears to two disciples on the road to Emmaus (Mark 16:12,13; Luke 24:13-35)
• Jesus appears to Peter ( Luke 24:34, 1 Corinthians 15:5)
• Jesus appears to his disciples, in Jerusalem. (Mark 16:14-18; Luke 24:36-49; John 20:19-23).
• Jesus again appears to his disciples, in Jerusalem. At this time Thomas is present (John 20:24-29).
• Jesus appears to his disciples on the shore of the Sea of Galilee (Matthew 28:16; John 21:1,2)
• Jesus is seen by 500 believers at one time (1 Corinthians 15:6)
• Jesus appears to James ( 1 Corinthians 15:7)
• Jesus appears to his disciples on a mountain in Galilee (Matthew 28:16-20).
• He appeared to his disciples (Luke 24:50-53).
• He appeared to Paul on the Damascus road (Acts 9:3-6; 1 Corinthians 15:8).
I will go ahead and offer some comments from various scholars and what they say about the appearances and the experiences of the disciples:
That Jesus’ followers (and later Paul) had resurrection experiences is, in my judgment, a fact. What the reality was that gave rise to the experiences I do not know. “I do not regard deliberate fraud as a worthwhile explanation. Many of the people in these lists were to spend the rest of their lives proclaiming that they had seen the risen Lord, and several of them would die for their cause. Moreover, a calculated deception should have produced great unanimity. Instead, there seem to have been competitors: ‘I saw him first!’ ‘No! I did.’ Paul’s tradition that 500 people saw Jesus at the same time has led some people to suggest that Jesus’ followers suffered mass hysteria. But mass hysteria does not explain the other traditions.” “Finally we know that after his death his followers experienced what they described as the ‘resurrection’: the appearance of a living but transformed person who had actually died. They believed this, they lived it, and they died for it.”
It is a historical fact that some of Jesus’ followers came to believe that he had been raised from the dead soon after his execution. We know some of these believers by name; one of them, the apostle Paul, claims quite plainly to have seen Jesus alive after his death. Thus, for the historian, Christianity begins after the death of Jesus, not with the resurrection itself, but with the belief in the resurrection.
Ehrman also says:
We can say with complete certainty that some of his disciples at some later time insisted that . . . he soon appeared to them, convincing them that he had been raised from the dead.
Ehrman also goes onto say:
Historians, of course, have no difficulty whatsoever speaking about the belief in Jesus’ resurrection, since this is a matter of public record.
Why, then, did some of the disciples claim to see Jesus alive after his crucifixion? I don’t doubt at all that some disciples claimed this. We don’t have any of their written testimony, but Paul, writing about twenty-five years later, indicates that this is what they claimed, and I don’t think he is making it up. And he knew are least a couple of them, whom he met just three years after the event (Galatians 1:18-19).
The disciples thought that they had witnessed Jesus’ appearances, which, however they are explained, “is a fact upon which both believer and unbeliever may agree.
Fuller goes onto say:
Even the most skeptical historian” must do one more thing: “postulate some other event” that is not the disciples’ faith, but the reason for their faith, in order to account for their experiences. Of course, both natural and supernatural options have been proposed. 
What did the disciples see? Let’s now look at some of the comments by how some scholars account for the appearances:
The historical ground of Easter is very simple: the followers of Jesus, both then and now, continued to experience Jesus as a living reality after his death. In the early Christian community, these experiences included visions or apparitions of Jesus. 
The real Easter faith is faith in the word of preaching which brings illumination. If the event of Easter is in any sense in historical event additional to the event of the Cross, it is nothing else than the rise of faith in the risen Lord, since is was this faith which led to the apostolic preaching. The resurrection itself is not an event of past history. All that historical criticism can establish is that the first disciples came to believe the resurrection.
John Dominic Crossan
When the evangelists spoke about the resurrection of Jesus, they told stories about apparitions or visions. People have visions…. there is nothing impossible about that. But were these post-resurrection stories accounts of historical visions or apparitions? What sort of narratives were they? Were they histories or parables? 
At the heart of the Christian religion lies a vision described in Greek by Paul as ophehe—-“he was seen.” And Paul himself, who claims to have witnessed an appearance asserted repeatedly “I have seen the Lord.” So Paul is the main source of the thesis that a vision is the origin of the belief in resurrection….When we talk about visions, we must include something that we experience every night when we dream. That’s our subconscious was of dealing with reality. A vision of that sort was at the heart of the Christian religion; and that vision, reinforced by enthusiasm, was contagious and led to many more visions, until we have an appearance to more than five hundred people. 
In his book The Resurrection of the Messiah, Christopher Bryan responds to Lüdemann:
One may grant that such visions as Lüdemann describes were common in antiquity and are so still—I will confess to having had two such experiences myself. Yet however common such visions may have been or are (and in sense, the commoner they were or are, the stronger this objection becomes) neither in antiquity nor in the present are they normally regarded as evidence of resurrection. On the contrary they are taken to be at worst hallucinations, and at best (as I take them to be) genuine communications of the comfort about the departed from beyond the grave. But in neither case are they considered to be declarations that the departed one has risen from the dead. That, however, is what the texts claim about Jesus. That is what Peter and Paul actually do say. Why do they do that? Lüdemann’s hypothesis leaves that question unanswered. Hence, it does not explain what Ludemann himself says needs to be explained. 
A few years back Ehrman released another book on Christology.
In the book he devotes two chapters to the resurrection. He tends to lean on the Lüdemann hypothesis that the disciples had visionary experiences. In it he says:
It is undisputable that some of the followers of Jesus came to think that he had been raised from the dead, and that something had to have happened to make them think so. Our earliest records are consistent on this point, and I think they provide us with the historically reliable information in one key aspect: the disciples’ belief in the resurrection was based on visionary experiences. I should stress it was visions, and nothing else, that led to the first disciples to believe in the resurrection. -Bart D. Ehrman, How Jesus Became God: The Exaltation of a Jewish Preacher from Galilee (New York: Harper One, 2014), 183-184.
So here Ehrman sides with the visionary language that Crossan, Borg and Lüdemann use. The good news is that Ehrman goes onto to define what he means by “visions” of Jesus. He describes visions as something that are either “veridical” or “nonveridical.” Veridical visions means people tend to see things that are really there while nonveridical visions the opposite-what a person sees is not based any kind of external reality. It is the latter that leads to what is called the hallucination hypothesis. In other words, skeptics assert that nonveridical visions can be attributed to some sort of psychological explanation. Ehrman then punts to his agnosticism again and says he doesn’t care if the appearances can be attributed to either “veridical” or “nonveridical” visionary experiences or anything else. This is rather confusing in that Ehrman first says it is visions that can explain the resurrection appearances. Given Ehrman and others like Lüdemann punt to the vision hypothesis, Bryan goes on to say the following about the quotes from Bultmann, Borg, and Crossan. Given Ehrman is saying something similar here. I think Bryan’s comments have relevance here as well:
If the experience of the first Christians was the kind of experience that Bultmann, Borg, and Crossan suggest—visionary and internal, simply the conversion of their hearts to God’s truth and the real meaning of Jesus life and death—then why on earth did they not say so? The language to describe such experiences was clearly available, so why did the first Christians not use it? Why did they choose instead to use the language of resurrection, words such as egeiro and anistemi, words which, we have noted, were normally used in quite different connections and whose use here was therefore inviting misunderstanding of experiences that would, in fact, have been perfectly acceptable to many in the ancient world who found resurrection ridiculous?” Why did the first Christians bring “resurrection” into their proclamation at all (other than future open)—unless they genuinely believed that something had happened that could be only be spoken of in this way? 
Building on what Bryan says, Peter Walker says:
“Resurrection” (anastasia )in Greek was a word which has already developed a clear meaning. It referred to a physical raising back to life within this world of those whom God chose –“the resurrection of the just” “on the last day” (cf. Matthew 22:28; John 11:24). So when the disciples claimed Resurrection for Jesus, they were claiming that God had done for one man what they were expecting him to do for all his faithful people at the end of time (what Paul refers to as the “hope” of Israel [Acts 23;26:6]. If they had meant merely that Jesus was a good fellow who did not deserve to die and whose effect on people would surely continue beyond his death, they would have used some other word. They would not have dared to use this word, which meant one thing and only one thing—God’s act of raising from physical death. That is what they meant. And that is what they would have been heard to mean. 
Furthermore, the use of the word “opethe” (the Greek word for appeared) shows the Gospel writers did believe that Jesus appeared physically. “There you will see (opethe) him” (Matt. 28:7); “The Lord has risen and has appeared (opethe) to Simon” (Luke 24:24). When they used “opethe” here, it means that He appeared physically to them. So when Paul gives his list of appearances in 1 Cor. 15:3-8, the issue becomes whether the appearance to him is the same as it was to the disciples. Bryan says:
There is no indication that he wants to regard the last item in that series as essentially different from the others. Second, he uses the word “opethe” of the appearances to himself as he uses of the appearances to the others. He regards it as the same kind. He saw the risen Lord as they did. There is no doubt the post resurrection body of Jesus (after the ascension) had to be somewhat different than the body the disciples saw. 
In the end, Ehrman doesn’t think Jesus rose from the dead. This is partially due to his interpretation of the burial story. He’s wrong here as well. Anyway, I still have great respect for Ehrman. Given he agrees in the post resurrection appearances, hopefully he will come to believe that the bodily resurrection is the best explanation for these appearances.
 E.P. Sanders , The Historical Figure of Jesus (New York: Penguin Books, 1993), 279-280.
 Bart Ehrman, The New Testament: A Historical Introduction to the Early Christian Writings, (Third Edition New York, Oxford: Oxford University Press, 2004), 276.
 Bart Ehrman, Jesus: Apocalyptic Prophet of the New Millennium (New York: Oxford University, 1999), 230
(4] Ibid, 231.
 Ehrman, The New Testament: An Historical Introduction to the Early Christian Writings, 282.
 Reginald Fuller, The Foundations of New Testament Christology (New York: Scribner’s, 1965), 142.
 Reginald Fuller, The Formation of the Resurrection Narratives (New York: Macmillan, 1980),
 Ibid, 2, 169, 181.
 Rudolph Bultmann, “The New Testament and Mythology,” in Kerygma and Myth: A Theological Debate, ed. Hans Werner Bartsch, trans. Reginald H. Fuller (London: S.P.C.K, 1953-62), 38, 42.
 John Dominic Crossan, A Long Way from Tipperary: A Memoir (San Francisco: HarperSanFransisco, 2000), 164-165.
 Gerd Lüdemann, The Resurrection of Jesus: History, Experience, Theology. Translated by John Bowden. London: SCM, 1994 (1994), 97, 100.
 Christopher Bryan, The Resurrection of the Messiah (Oxford University Press, USA, 2011), 163-164.
 Ibid, 169-170.
 P.W. Walker, The Weekend That Changed the World (Louisville, KY: Westminster John Knox, 1999), 63.
 Bryan, The Resurrection of the Messiah, 53.